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

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.