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Uniqueness of Shalika Models

Published online by Cambridge University Press:  20 November 2018

Chufeng Nien
Chufeng Nien*
Affiliation:
Department of Mathematics, National Cheng Kung University, Tainan 701, Taiwan email: nienpig@mail.ncku.edu.tw
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Abstract

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Let ${{\mathbb{F}}_{q}}$ be a finite field of $q$ elements, $\mathcal{F}$ a $p$-adic field, and $D$ a quaternion division algebra over $\mathcal{F}$. This paper proves uniqueness of Shalika models for $\text{G}{{\text{L}}_{2n}}\left( {{\mathbb{F}}_{q}} \right)$ and $\text{G}{{\text{L}}_{2n}}\left( D \right)$, and re-obtains uniqueness of Shalika models for $\text{G}{{\text{L}}_{2n}}\left( \mathcal{F} \right)$ for any $n\,\in \,\mathbb{N}$.

Keywords

22E50Shalika modelslinear modelsuniquenessmultiplicity free
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 61 , Issue 6 , 01 December 2009 , pp. 1325 - 1340
Copyright
Copyright © Canadian Mathematical Society 2009

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