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arXiv · 1708.08111

A Combinatorial Formula for Test Functions with Pro-p Iwahori Level Structure

Marc Horn
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Abstract

The Test Function Conjecture due to Haines and Kottwitz predicts that the geometric Bernstein center is a source of test functions required by the Langlands-Kottwitz method for expressing the local semisimple Hasse-Weil zeta function of a Shimura variety in terms of automorphic L-functions. Haines and Rapoport found an explicit formula for such test functions in the Drinfeld case with pro-p Iwahori level structure. This article generalizes the Haines-Rapoport formula for the Drinfeld case to a broader class of split groups. The main theorem presents a new formula for test functions with pro-p Iwahori level structure, which can be computed through some combinatorics on Coxeter groups. Explicit descriptions of the test function in certain low-rank general linear and symplectic group examples are included.

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BibTeXRIS

Marc Horn. 2017-08-27. A Combinatorial Formula for Test Functions with Pro-p Iwahori Level Structure. https://arxiv.org/abs/1708.08111

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