Maxim Gurevich
Published 2024-05-27Version 1
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.
Comments: to appear in the IMS Lecture Note Series for "Representations and Characters: Revisiting the Works of Harish-Chandra and Andr\'e Weil"
On Isotropic Bessel Models for Principal Series Representations of $SO_{n,n+1}(\Bbb R)$
Positivity of principal matrix coefficients of principal series representations of $GL_{n}(R)$
On extensions of principal series representations
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