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arXiv · 2201.01146

A triangular system for local character expansions of Iwahori-spherical representations of general linear groups

Maxim Gurevich
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Abstract

For Iwahori-spherical representations of non-Archimedean general linear groups, Chan-Savin recently expressed the Whittaker functor as a restriction to an isotypic component of a finite Iwahori-Hecke algebra module. We generalize this method to describe principal degenerate Whittaker functors. Concurrently, we view Murnaghan's formula for the Harish-Chandra--Howe character as a Grothendieck group expansion of the same module. Comparing the two approaches through the lens of Zelevinsky's PSH-algebras, we obtain an explicit unitriangular transition matrix between coefficients of the character expansion and the principal degenerate Whittaker dimensions.

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Maxim Gurevich. 2022-01-04. A triangular system for local character expansions of Iwahori-spherical representations of general linear groups. https://arxiv.org/abs/2201.01146

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