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arXiv · 2312.10845

A local twisted trace formula for Whittaker induction of coregular symmetric pairs: the geometric side

Raphaël Beuzart-Plessis·Chen Wan
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Abstract

In this paper, we prove the geometric expansion of a local twisted trace formula for the Whittaker induction of any symmetric pairs that are coregular. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur \cite{A91} and Waldspurger \cite{WalFTLtordue}. We also prove a formula for the regular germs of quasi-characters associated to strongly cuspidal functions in terms of certain weighted orbital integrals. As a consequence of our trace formula and the formula for regular germs of quasi-characters, we prove a simple local trace formula of those models for strongly cuspidal test functions which implies a multiplicity formula for these models. We also present various applications of our trace formula and multiplicity formula, including a necessary condition for a discrete L-packet to contain a representation with a unitary Shalika model (resp. a Galois model for classical groups) in terms of the associated Langlands parameter, and we also compute the summation of the corresponding multiplicities for certain discrete L-packets.

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Raphaël Beuzart-Plessis, Chen Wan. 2024-06-13. A local twisted trace formula for Whittaker induction of coregular symmetric pairs: the geometric side. https://arxiv.org/abs/2312.10845

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