XMU/XMUM Joint Mathematics Online Seminar: Endoscopic liftings of supercuspidal representations for classical groups

：Tam Kam Fai（厦门大学马来西亚分校）
：2025-05-19 15:30
：腾讯会议ID: 792-302-653（无密码）

报告人：Tam Kam Fai（厦门大学马来西亚分校）

时  间：2025年5月19日15:30

地  点：腾讯会议ID: 792-302-653（无密码）

内容摘要:

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. 

个人简介：

Dr. Kam Fai Tam is an Associate Professor at Xiamen University Malaysia. Dr. Kam Fai Tam received his PhD at the University of Toronto in 2012. He received his Master and Bachelor at the Hong Kong University of Science and Technology.