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arXiv · 2608.24836

Kloosterman sheaves and Bessel functions for generic principal series of finite groups

Robert Cass·Miao Pam Gu·Elad Zelingher
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Abstract

Let $G$ be a quasi-split reductive group over a finite field and let $\^G$ be the Langlands dual group. Assuming the derived subgroup of $G$ is almost simple, we use techniques from the geometric Langlands program to relate special values of Bessel functions for generic principal series representations of $G$ to the trace of Frobenius acting on Kloosterman sheaves of Heinloth-Ng\^o-Yun for $\^G$. We also give explicit examples in essentially all possible cases, including exceptional groups.

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BibTeXRIS

Robert Cass, Miao Pam Gu, Elad Zelingher. 2026-08-25. Kloosterman sheaves and Bessel functions for generic principal series of finite groups. https://arxiv.org/abs/2608.24836

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