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

Roger Plymen

doi:10.4064/bc120-1

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

Roger Plymen

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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.

Original language	English
Title of host publication	Proceedings of conference on Quantum Dynamics
Place of Publication	Poland
Publisher	Banach Center Publications
Pages	11-21
Volume	120
DOIs	https://doi.org/10.4064/bc120-1
Publication status	E-pub ahead of print - 1 Sep 2020

Keywords

math.RT
20G25, 22E50

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10.4064/bc120-1Licence: Unspecified

1606.01497v3

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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. ",

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

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Keywords

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