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

Xuantong Qu

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

Representation Theory 2022-09-09 v1

Authors: Xuantong Qu

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)$.

Keywords

curtis homomorphisms gelfand-tsetlin diagrams whittaker functions principal series representations gauss-bruhat decomposition gl(n,f_q)

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@article{arxiv.2209.03389,
  title  = {On explicit computation of Curtis homomorphisms for $GL(n,\mathbb{F}_q)$},
  author = {Xuantong Qu},
  journal= {arXiv preprint arXiv:2209.03389},
  year   = {2022}
}

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19 pages

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

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