Prof Roger Plymen MA, DPhil (Oxon)

Emeritus Professor

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Publications

  1. 2021
  2. Published

    Comparison of the depths on both sides of the local Langlands correspondence for Weil-restricted groups

    Plymen, R. & Aubert, A-M., 28 Dec 2021, In: Journal of Number Theory. 233 (2022), p. 24-58

    Research output: Contribution to journalArticlepeer-review

  3. 2020
  4. E-pub ahead of print

    Epsilon factors as algebraic characters on the smooth dual of $\mathrm{GL}_n$

    Plymen, R., 1 Sep 2020, (E-pub ahead of print) Proceedings of conference on Quantum Dynamics. Poland: Banach Center Publications, Vol. 120. p. 11-21

    Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

  5. Published

    The Great Prime Number Race

    Plymen, R., 13 Aug 2020, Rhode Island: American Mathematical Society. 152 p. (Student Mathematical Library)

    Research output: Book/ReportBookpeer-review

  6. Published

    Morita equivalence for k-algebras

    Plymen, R., Aubert, A-M., Baum, P. & Solleveld, M., 2020, Proceedings of conference on Quantum Dynamics. Warsaw: Banach Center Publications, Vol. 120. p. 245 - 265 21 p. (Banach Center Publications).

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

  7. 2019
  8. Published

    Contribution to Celebratio Mathematica

    Aubert, A-M., Plymen, R. & Solleveld, M., 15 Nov 2019, 20 p. Mathematical Sciences Publishers.

    Research output: Other contributionpeer-review

  9. Published

    Smooth duals of inner forms of GL_n and SL_n

    Plymen, R., Baum, P., Aubert, A-M. & Solleveld, M., 1 May 2019, In: Documenta Mathematica. 24, p. 373-420

    Research output: Contribution to journalArticlepeer-review

  10. Published

    Stratified Langlands duality in the A_n tower

    Plymen, R., Niblo, G. & Wright, N., 2019, In: Journal of Noncommutative Geometry. 13, p. 193-225

    Research output: Contribution to journalArticlepeer-review

  11. 2018
  12. Published

    Poincare' duality and Langlands duality for extended affine Weyl groups

    Plymen, R., Niblo, G. & Wright, N., 2018, In: Annals of K-theory. 3, 3, p. 491-522

    Research output: Contribution to journalArticlepeer-review

  13. Published

    The Skewes Number

    Plymen, R., 2018, USA: American Mathematical Society. 76 p. (AMS Open Math Notes)

    Research output: Book/ReportBookpeer-review

  14. 2017
  15. Published

    Conjectures about p-adic groups and their non commutative geometry

    Plymen, R., Aubert, A-M., Baum, P. & Solleveld, M., 1 Jan 2017, In: Contemporary Mathematics. 691, p. 15-51

    Research output: Contribution to journalArticlepeer-review

  16. Published

    Functoriality and K-theory for GL_n(R)

    Plymen, R. & Mendes, S., 2017, In: Munster Journal of Mathematics. 10, p. 39-58

    Research output: Contribution to journalArticlepeer-review

  17. Published

    Hecke algebras for inner forms of p-adic special linear groups

    Plymen, R., Aubert, A-M., Baum, P. & Solleveld, M., 2017, In: Journal de l'Institut Mathématiques Jussieu. 16, 2, p. 351-419

    Research output: Contribution to journalArticlepeer-review

  18. Published

    On L-packets and depth for SL_2(K) and its inner form

    Plymen, R., Aubert, A-M., Mendes, S. & Solleveld, M., 2017, In: International Journal of Number Theory. 13, p. 1-19

    Research output: Contribution to journalArticlepeer-review

  19. Published

    The principal series of p -adic groups with disconnected center

    Aubert, A. M., Baum, P., Plymen, R. & Solleveld, M., 2017, In: Proceedings of the London Mathematical Society. 114, 5, p. 798-854 57 p.

    Research output: Contribution to journalArticlepeer-review

  20. 2016
  21. Published

    The local Langlands correspondence for inner forms of SL_n

    Plymen, R., Aubert, A-M., Baum, P. & Solleveld, M., 5 Dec 2016, In: Research in the Mathematical Sciences . 3:32, p. 1 34 p.

    Research output: Contribution to journalArticlepeer-review

  22. Published

    Geometric structure for the principal series of a reductive p-adic group with connected centre

    Plymen, R., Aubert, A-M., Baum, P. & Solleveld, M., 2016, In: Journal of Noncommutative Geometry. 10, 2, p. 663-680

    Research output: Contribution to journalArticlepeer-review

  23. Published

    The local spectrum of the Dirac operator for the universal cover of SL_2(R)

    Plymen, R., Brodzki, J., Niblo, G. & Wright, N., 2016, In: Journal of Functional Analysis. 270, 3, p. 957-975

    Research output: Contribution to journalArticlepeer-review

  24. 2014
  25. Published

    Geometric structure in smooth dual and local Langlands conjecture

    Aubert, A-M., Baum, P., Plymen, R. & Solleveld, M., Sep 2014, In: Japanese Journal of Mathematics. 9, 2, p. 99-136

    Research output: Contribution to journalArticlepeer-review

  26. 2013
  27. Published

    Depth and the local Langlands correspondence

    Aubert, A-M., Baum, P., Plymen, R. & Solleveld, M., Nov 2013, In: Progress in Mathematics. 319, p. 17-41 25 p.

    Research output: Contribution to journalArticlepeer-review

  28. Published

    On the local Langlands correspondence for non-tempered representations

    Aubert, A-M., Baum, P., Plymen, R. & Solleveld, M., Oct 2013, In: Munster Journal of Mathematics.

    Research output: Contribution to journalArticlepeer-review

  29. Published

    The local Langlands correspondence for inner forms of SLn

    Aubert, A-M., Baum, P., Plymen, R. & Solleveld, M., May 2013, In: MIMS EPrints. 2013.38.

    Research output: Contribution to journalArticlepeer-review

  30. Published

    K-theory and the connection index

    Kamran, T. & Plymen, R., Feb 2013, In: Bulletin of the London Mathematical Society. 45, 1, p. 111-119 8 p.

    Research output: Contribution to journalArticlepeer-review

  31. Published

    L-packets and formal degrees for SL_2(K) with K a local function field of characteristic 2

    Mendes, S. & Plymen, R., Feb 2013, In: Unknown Journal.

    Research output: Contribution to journalArticlepeer-review

  32. 2012
  33. Published

    Geometric structure in the tempered dual of SL(4)

    Chao, K. F. & Plymen, R., Jun 2012, In: Bulletin of the London Mathematical Society. 44, 3, p. 460-468 8 p.

    Research output: Contribution to journalArticlepeer-review

  34. 2011
  35. Published

    Geometric structure in the principal series of the {$p$}-adic group {${\rm G}_2$}

    Aubert, A-M., Baum, P. & Plymen, R., 2011, In: Representation Theory . 15, p. 126-169 44 p.

    Research output: Contribution to journalArticlepeer-review

  36. Published

    Geometric structure in the representation theory of reductive $p$-adic groups II

    Aubert, A-M., Baum, P. & Plymen, R., 2011, Harmonic analysis on reductive, $p$-adic groups. American Mathematical Society, Vol. 543. p. 71-90 20 p. (Contemp. Math.).

    Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

  37. 2010
  38. Published

    A new bound for the smallest x with π(x) > li(x)

    Chao, K. F. & Plymen, R., May 2010, In: International Journal of Number Theory. 6, 3, p. 681-690 9 p.

    Research output: Contribution to journalArticlepeer-review

  39. Published

    R-groups and geometric structure in the representation theory of SL(N)

    Jawdat, J. & Plymen, R., 2010, In: Journal of Noncommutative Geometry. 4, 2, p. 265-279 14 p.

    Research output: Contribution to journalArticlepeer-review

  40. 2007
  41. Published

    Geometric structure in the representation theory of p-adic groups

    Aubert, A. M., Baum, P. & Plymen, R., 15 Nov 2007, In: Académie des Sciences. Comptes Rendus. Mathématique. 345, 10, p. 573-578 5 p.

    Research output: Contribution to journalArticlepeer-review

  42. Published

    Base change and $K$-theory for $\rm GL(n)$

    Mendes, S. & Plymen, R., 2007, In: Journal of Noncommutative Geometry. 1, 3, p. 311-331

    Research output: Contribution to journalArticlepeer-review

  43. 2006
  44. Published

    Cycles in the chamber homology of GL(3)

    Aubert, A. M., Hasan, S. & Plymen, R., Apr 2006, In: K-Theory. 37, 4, p. 341-377 36 p.

    Research output: Contribution to journalArticlepeer-review

  45. Published

    The Hecke algebra of a reductive $p$-adic group: a geometric conjecture

    Aubert, A-M., Baum, P. & Plymen, R., 2006, Noncommutative geometry and number theory. p. 1-34 (Noncommutative geometry and number theory).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  46. 2005
  47. Published

    Plancherel measure for GL(n, F) and GL(m, D): Explicit formulas and Bernstein decomposition

    Aubert, A. M. & Plymen, R., May 2005, In: Journal of Number Theory. 112, 1, p. 26-66 40 p.

    Research output: Contribution to journalArticlepeer-review

  48. Published

    Entire cyclic cohomology of Schatten ideals

    Plymen, R., Brodzki, J. & Flymen, R., 2005, In: Homology, Homotopy and Applications. 7, 3, p. 37-52 15 p.

    Research output: Contribution to journalArticlepeer-review

  49. 2004
  50. Published

    Formule de Plancherel explicite pour le groupe p-adique

    Aubert, A. M. & Plymen, R., 1 Jun 2004, In: Académie des Sciences. Comptes Rendus. Mathématique. 338, 11, p. 843-848 5 p.

    Research output: Contribution to journalArticlepeer-review

  51. 2003
  52. Published

    Local-global principle for the Baum-Connes conjecture with coefficients

    Baum, P., Millington, S. & Plymen, R., 2003, In: K-Theory. 28, 1, p. 1-18 17 p.

    Research output: Contribution to journalArticlepeer-review

  53. 2002
  54. Published

    Reduced C*-algebra of the p-adic group GL(n) II

    Plymen, R. J., 1 Dec 2002, In: Journal of Functional Analysis. 196, 1, p. 119-134 15 p.

    Research output: Contribution to journalArticlepeer-review

  55. Published

    Chern character for the Schwartz algebra of p-adic GL(n)

    Brodzki, J. & Plymen, R., Mar 2002, In: Bulletin of the London Mathematical Society. 34, 2, p. 219-228 9 p.

    Research output: Contribution to journalArticlepeer-review

  56. Published

    Complex structure on the smooth dual of $\rm GL(n)$

    Brodzki, J. & Plymen, R., 2002, In: Doc. Math.. 7, p. 91-112

    Research output: Contribution to journalArticlepeer-review

  57. 2001
  58. Published

    Une démonstration de la conjecture de Baum-Connes pour les groupes réductifs adèliques

    Plymen, R., Baum, P., Millington, S. & Flymen, R., 1 Feb 2001, In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 332, 3, p. 195-200 5 p.

    Research output: Contribution to journalArticlepeer-review

  59. 2000
  60. Published

    Geometry of the smooth dual of $\rm GL(n)$

    Brodzki, J. & Plymen, R., 2000, In: C. R. Acad. Sci. Paris Sér. I Math.. 331, 3, p. 213-218

    Research output: Contribution to journalArticlepeer-review

  61. Published

    Representation theory of $p$-adic groups: a view from operator algebras

    Baum, P. F., Higson, N. & Plymen, R. J., 2000, The mathematical legacy of Harish-Chandra (Baltimore, MD, 1998). Vol. 68. p. 111-149 (The mathematical legacy of Harish-Chandra (Baltimore, MD, 1998)).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  62. 1999
  63. Published

    Homologie cyclique périodique de certaines algèbres nucléaires

    Brodzki, J. & Plymen, R., 15 Oct 1999, In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics. 329, 8, p. 671-676 5 p.

    Research output: Contribution to journalArticlepeer-review

  64. 1997
  65. Published

    A proof of the Baum-Connes conjecture for $p$-adic $\rm GL(n)$

    Baum, P., Higson, N. & Plymen, R., 1997, In: C. R. Acad. Sci. Paris Sér. I Math.. 325, 2, p. 171-176

    Research output: Contribution to journalArticlepeer-review

  66. Published

    Universal example for $S$-arithmetic groups

    Hodgins, J. E. & Plymen, R. J., 1997, In: Exposition. Math.. 15, 2, p. 149-159

    Research output: Contribution to journalArticlepeer-review

  67. 1996
  68. Published

    The representation theory of $p$-adic $\rm GL(n)$ and Deligne-Langlands parameters

    Hodgins, J. E. & Plymen, R. J., 1996, Analysis, geometry and probability. Vol. 10. p. 54-72 (Analysis, geometry and probability).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  69. 1994
  70. Published

    Spinors in Hilbert space

    Plymen, R. J. & Robinson, P. L., 1994, Cambridge University Press. (Cambridge Tracts in Mathematics)

    Research output: Book/ReportBookpeer-review

  71. 1993
  72. Published

    Equivariant homology for $\rm SL(2)$ of a $p$-adic field

    Baum, P., Higson, N. & Plymen, R., 1993, Index theory and operator algebras (Boulder, CO, 1991). Vol. 148. p. 1-18 (Index theory and operator algebras (Boulder, CO, 1991)).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  73. 1992
  74. Published

    Coupling constants for $p$-adic groups

    Plymen, R. J., 1992, $p$-adic methods and their applications. p. 63-72 ($p$-adic methods and their applications).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  75. Published

    Elliptic representations and $K$-theory for $\rm SL(l)$

    Plymen, R. J., 1992, In: Houston Journal of Mathematics. 18, 1, p. 25-32

    Research output: Contribution to journalArticlepeer-review

  76. 1991
  77. Published

    $L\sp 2$-Fourier transform for reductive $p$-adic groups

    Leung, C. W. & Plymen, R. J., 1991, In: Bull. London Math. Soc.. 23, 2, p. 146-152

    Research output: Contribution to journalArticlepeer-review

  78. Published

    Arithmetic aspect of operator algebras

    Plymen, R. J. & Leung, C. W., 1991, In: Compositio Math.. 77, 3, p. 293-311

    Research output: Contribution to journalArticlepeer-review

  79. 1990
  80. Published

    Equivalence bimodules in the representation theory of reductive groups

    Plymen, R. J., 1990, Operator theory. Vol. 51. p. 267-272 (Operator theory).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  81. Published

    Reduced $C\sp *$-algebra for reductive $p$-adic groups

    Plymen, R. J., 1990, In: Journal of Functional Analysis. 88, 2, p. 251-266

    Research output: Contribution to journalArticlepeer-review

  82. 1987
  83. Published

    Complex conformal rescaling and Spin-structure

    Plymen, R. J. & Westbury, B. W., 1987, In: Bull. London Math. Soc.. 19, 4, p. 363-370

    Research output: Contribution to journalArticlepeer-review

  84. Published

    The reduced $C\sp \ast$-algebra of the $p$-adic group $\rm GL(n)$

    Plymen, R. J., 1987, In: Journal of Functional Analysis. 72, 1, p. 1-12

    Research output: Contribution to journalArticlepeer-review

  85. 1986
  86. Published

    Strong Morita equivalence, spinors and symplectic spinors

    Plymen, R. J., 1986, In: Journal of Operator Theory. 16, 2, p. 305-324

    Research output: Contribution to journalArticlepeer-review

  87. 1985
  88. Published

    $K$-theory of the reduced $C\sp \ast$-algebra of $\rm SL\sb 2(\bf Q\sb p)$

    Plymen, R. J., 1985, Operator algebras and their connections with topology and ergodic theory (Bu\c steni, 1983). Vol. 1132. p. 409-420 (Operator algebras and their connections with topology and ergodic theory (Bu\c steni, 1983)).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  89. 1983
  90. Published

    The dirac operator and the principal series for complex semisimple lie groups

    Penington, M. G. & Plymen, R. J., 1 Oct 1983, In: Journal of Functional Analysis. 53, 3, p. 269-286 17 p.

    Research output: Contribution to journalArticlepeer-review

  91. 1982
  92. Published

    The Weyl bundle

    Plymen, R. J., Nov 1982, In: Journal of Functional Analysis. 49, 2, p. 186-197 11 p.

    Research output: Contribution to journalArticlepeer-review

  93. 1980
  94. Published

    Cyclotomic integers and the inner invariant of Connes

    Plymen, R. J., 1980, In: Journal of the London Mathematical Society. 22, 1, p. 14-20

    Research output: Contribution to journalArticlepeer-review

  95. Published

    On the outer and inner invariants of Connes

    Parthasarathy, K. R. & Plymen, R. J., 1980, In: Journal of Functional Analysis. 38, 1, p. 1-15

    Research output: Contribution to journalArticlepeer-review

  96. Published

    The Laplacian and the Dirac operator in infinitely many variables

    Plymen, R. J., 1980, In: Compositio Math.. 41, 1, p. 137-152

    Research output: Contribution to journalArticlepeer-review

  97. 1979
  98. Published

    Automorphic group representations: a new proof of Blattner’s theorem

    de la Harpe, P. & Plymen, R. J., 1979, In: Journal of the London Mathematical Society. 19, 3, p. 509-522

    Research output: Contribution to journalArticlepeer-review

  99. Published

    Automorphic group representations: the hyperfinite $\rm II\sb1$ factor and the Weyl algebra

    Plymen, R. J., 1979, Algèbres d’opérateurs (Sém., Les Plans-sur-Bex, 1978). Vol. 725. p. 291-306 (Algèbres d’opérateurs (Sém., Les Plans-sur-Bex, 1978)).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  100. Published

    Some recent results on infinite-dimensional spin groups

    Plymen, R. J., 1979, Studies in algebra and number theory. Vol. 6. p. 159-171 (Studies in algebra and number theory).

    Research output: Chapter in Book/Report/Conference proceedingChapter

  101. 1977
  102. Published

    Projective representations of the infinite orthogonal group

    Plymen, R. J., 1977, In: Mathematika. 24, 1, p. 115-121

    Research output: Contribution to journalArticlepeer-review

  103. 1976
  104. Published

    A variant of the fundamental theory of projective geometry

    Plymen, R. J. & Williams, C. M., 1976, In: Mathematika. 23, 1, p. 89-93

    Research output: Contribution to journalArticlepeer-review

  105. Published

    On the Weyl character formula for $\rm SU(n)$

    Plymen, R. J., 1976, In: Internat. J. Theoret. Phys.. 15, 3, p. 201-206

    Research output: Contribution to journalArticlepeer-review

  106. Published

    Spinors in Hilbert space

    Plymen, R. J., 1976, In: Math. Proc. Cambridge Philos. Soc.. 80, 2, p. 337-347

    Research output: Contribution to journalArticlepeer-review

  107. 1975
  108. Published

    A model of the universal covering group of $\rm SO(H)\sb2$

    Plymen, R. J. & Streater, R. F., 1975, In: Bull. London Math. Soc.. 7, 3, p. 283-288

    Research output: Contribution to journalArticlepeer-review

  109. 1974
  110. Published

    On the spin algebra of a real Hilbert space

    Plymen, R. J. & Young, R. M. G., 1974, In: Journal of the London Mathematical Society. 9, p. 286-292

    Research output: Contribution to journalArticlepeer-review

  111. 1973
  112. Published

    Two-state systems and the two-sphere

    Plymen, R., 1973, In: Il Nuovo Cimento B. 13, 1, p. 55-58 4 p.

    Research output: Contribution to journalArticlepeer-review

  113. 1968
  114. Published

    Dispersion-free normal states

    Plymen, R. J., 1 Apr 1968, In: Il Nuovo Cimento A. 54, 4, p. 862-870 9 p.

    Research output: Contribution to journalArticlepeer-review

  115. Published

    $C\sp\ast $-algebras and Mackey’s axioms

    Plymen, R. J., 1968, In: Comm. Math. Phys.. 8, p. 132-146

    Research output: Contribution to journalArticlepeer-review

  116. Published

    A modification of Piron’s axioms

    Plymen, R. J., 1968, In: Helvetica Physica Acta . 41, p. 69-74

    Research output: Contribution to journalArticlepeer-review

  117. 1961
  118. Published

    A model of the arithmetic of alephs in the equation calculus

    Plymen, R. J., 1961, In: Zeitschrift fuer Mathematische Logik und Grundlagen der Mathematik. 7, p. 257-258

    Research output: Contribution to journalArticlepeer-review

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