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# Uniqueness of Shalika Models

Published:2009-12-01
Printed: Dec 2009
• Chufeng Nien
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## Abstract

Let $\BF_q$ be a finite field of $q$ elements, $\CF$ a $p$-adic field, and $D$ a quaternion division algebra over $\CF$. This paper proves uniqueness of Shalika models for $\GL_{2n}(\BF_q)$ and $\GL_{2n}(D)$, and re-obtains uniqueness of Shalika models for $\GL_{2n}(\CF)$ for any $n\in \BN$.
 Keywords: Shalika models, linear models, uniqueness, multiplicity free
 MSC Classifications: 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]