On explicit computation of Curtis homomorphisms for $GL(n,\mathbb{F}_q)$

Xuantong Qu

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arXiv · 2209.03389

On explicit computation of Curtis homomorphisms for $GL(n,\mathbb{F}_q)$

Xuantong Qu

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Abstract

In this note we give explicit computations of certain types of Curtis homomorphisms and interpret them in terms of Gelfand-Tsetlin diagrams. Namely, this interpretation follows from Gelfand-Tsetlin formulas for the $GL(n,\mathbb{F}_q)$-Whittaker functions associated with principal series representations via exploiting the method in arXiv:0705.2886 for $GL(n,\mathbb{$})$-Whittaker functions. The explicit computations of Whittaker functions are based on computing the Gauss-Bruhat decomposition for certain elements in $GL(n,\mathbb{F}_q)$.

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Xuantong Qu. 2022-09-07. On explicit computation of Curtis homomorphisms for $GL(n,\mathbb{F}_q)$. https://arxiv.org/abs/2209.03389

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