Row and column removal rules for finite unitary groups
数学专题报告
报告题目(Title)： Row and column removal rules for finite unitary groups
报告人(Speaker)：Pengcheng Li (Tsinghua university)
地点(Place)：后主楼1220
时间(Time)：2025年9月24日 （周三）16:30-17:30
邀请人(Inviter)： 肖杰、覃帆、周宇
报告摘要
In the 1980s, James provided a construction of the l-modular unipotent irreducible representations of the finite general linear groups GL(n,q), along with the row and column removal rules for computing the decomposition numbers. In ongoing joint work with Olivier Dudas, we aim to extend this framework to the case of finite unitary groups. In this setting, Harish-Chandra induction is replaced by the Howe correspondence, while degenerate Gelfand–Graev representations are replaced by generalized Gelfand–Graev representations. We expect that the shadow of relative Langlands duality in the modular representation theory of finite classical groups will manifest through a combination of row–column duality and simple–projective duality. In addition, we have discovered an interesting connection with the bow variety and S duality.
