On explicit computation of Curtis homomorphisms for GL(n,\mathbbF_q)

2022/09/07 by Qu, Xuantong
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2209.03389

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,\mathbbF_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,\mathbbF_q).

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