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

DOI10.5802/CRMATH.384arXiv2201.01146MaRDI QIDQ6387471

Publication date: 4 January 2022

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.

Mathematics Subject Classification ID

Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

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