Speaker：Tam Kam Fai (Xiamen University Malaysia)

Time：2025-5-19, 15:30

Location：Tencent Meeting ID：792-302-653（No Password） 

Abstract:

Let G be a classical group (orthogonal, symplectic, or unitary) over a p-adic field F, and π be a supercuspidal representation of G(F). We propose a general strategy to express the Langlands parameter of π, only requiring the residual characteristic p to be odd, with proven examples by the speaker (partly joint with Corinne Blondel) and others. To briefly explain the strategy, we apply M{\oe}glin’s theory of Jordan blocks and Bushnell-Kutzko’s theory of covering types to determine the endoscopic lift of π into the general linear group whose dual expresses the dual group of G as a complex matrix group. The cuspidal support of this lifted representation is expressed in terms of the inducing type of π defined by Stevens’ construction of supercuspidal representations using skew semi-simple strata. This strategy is completely on the representation side.