A local twisted trace formula for Whittaker induction of coregular symmetric pairs: the geometric side
| Autor: | Beuzart-Plessis, Raphaël, Wan, Chen |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 137 pages, comments are welcome |
| Databáze: | arXiv |
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