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Uniqueness of Shalika Models
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- Journal:
- Canadian Journal of Mathematics / Volume 61 / Issue 6 / 01 December 2009
- Published online by Cambridge University Press:
- 20 November 2018, pp. 1325-1340
- Print publication:
- 01 December 2009
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- Article
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- You have access
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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 
$n\,\in \,\mathbb{N}$.
