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

Standard

Proceedings of conference on Quantum Dynamics. Vol. 120 Poland : Banach Center Publications, 2020. p. 11-21.

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

Harvard

Plymen, R 2020, Epsilon factors as algebraic characters on the smooth dual of $\mathrm{GL}_n$. in Proceedings of conference on Quantum Dynamics. vol. 120, Banach Center Publications, Poland, pp. 11-21. https://doi.org/10.4064/bc120-1

APA

Plymen, R. (2020). Epsilon factors as algebraic characters on the smooth dual of $\mathrm{GL}_n$. In Proceedings of conference on Quantum Dynamics (Vol. 120, pp. 11-21). Banach Center Publications. https://doi.org/10.4064/bc120-1

Vancouver

Plymen R. Epsilon factors as algebraic characters on the smooth dual of $\mathrm{GL}_n$. In Proceedings of conference on Quantum Dynamics. Vol. 120. Poland: Banach Center Publications. 2020. p. 11-21 https://doi.org/10.4064/bc120-1

Author

Plymen, Roger. / Epsilon factors as algebraic characters on the smooth dual of $\mathrm{GL}_n$. Proceedings of conference on Quantum Dynamics. Vol. 120 Poland : Banach Center Publications, 2020. pp. 11-21

Bibtex

@inbook{d0f9d60454f64720a2a625a02eb8bcdc,
title = "Epsilon factors as algebraic characters on the smooth dual of $\mathrm{GL}_n$",
abstract = " Let $K$ be a non-archimedean local field and let $G = \mathrm{GL}_n(K)$. We have shown in previous work that the smooth dual $\mathbf{Irr}(G)$ admits a complex structure: in this article we show how the epsilon factors interface with this complex structure. The epsilon factors, up to a constant term, factor as invariant characters through the corresponding complex tori. For the arithmetically unramified smooth dual of $\mathrm{GL}_n$, we provide explicit formulas for the invariant characters. ",
keywords = "math.RT, 20G25, 22E50",
author = "Roger Plymen",
note = "12 pages. Minor improvements, new title",
year = "2020",
month = sep,
day = "1",
doi = "10.4064/bc120-1",
language = "English",
volume = "120",
pages = "11--21",
booktitle = "Proceedings of conference on Quantum Dynamics",
publisher = "Banach Center Publications",

}

RIS

TY - CHAP

T1 - Epsilon factors as algebraic characters on the smooth dual of $\mathrm{GL}_n$

AU - Plymen, Roger

N1 - 12 pages. Minor improvements, new title

PY - 2020/9/1

Y1 - 2020/9/1

N2 - Let $K$ be a non-archimedean local field and let $G = \mathrm{GL}_n(K)$. We have shown in previous work that the smooth dual $\mathbf{Irr}(G)$ admits a complex structure: in this article we show how the epsilon factors interface with this complex structure. The epsilon factors, up to a constant term, factor as invariant characters through the corresponding complex tori. For the arithmetically unramified smooth dual of $\mathrm{GL}_n$, we provide explicit formulas for the invariant characters.

AB - Let $K$ be a non-archimedean local field and let $G = \mathrm{GL}_n(K)$. We have shown in previous work that the smooth dual $\mathbf{Irr}(G)$ admits a complex structure: in this article we show how the epsilon factors interface with this complex structure. The epsilon factors, up to a constant term, factor as invariant characters through the corresponding complex tori. For the arithmetically unramified smooth dual of $\mathrm{GL}_n$, we provide explicit formulas for the invariant characters.

KW - math.RT

KW - 20G25, 22E50

U2 - 10.4064/bc120-1

DO - 10.4064/bc120-1

M3 - Chapter

VL - 120

SP - 11

EP - 21

BT - Proceedings of conference on Quantum Dynamics

PB - Banach Center Publications

CY - Poland

ER -