On local character expansions for principal series representations of general linear groups

2024/05/27 by Maxim Gurevich, Gurevich, Maxim
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2405.16872

Abstract

We obtain two explicit formulas for the full local character expansion of any irreducible representation of a p-adic general linear group in principal blocks. The first, generalizing previous work of the author on the Iwahori-spherical case, expresses the expansion in terms of dimensions of degenerate Whittaker models. The second gives a closed expression in terms of values of Kazhdan-Lusztig polynomials of a suitable permutation group.

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