数学学科2019系列学术报告之二十五

报告题目：Irreducible modules of reductive groups with frobenius maps with B-stable line
报告人：陈晓煜，博士，上海师范大学
报告时间：2019年12月20日（周五）14:00-15:00
报告地点：1-232
摘要：
Let G be a connected reductive group defifined over Fp and B be a Borel subgroup of G (not necessarily defifined over Fp). Let k be an algebraically closed fifield of characteristic p > 0. We show that for each (one dimensional) character θ of B (not necessarily rational), there is an unique (up to isomorphism) irreducible kG-module L(θ) containing θ as a kB-submodule, and moreover, L(θ) is isomorphic to a parabolic induction from a fifinite dimensional irreducible kL-module, where L is a Levi subgroup of G. Thus, we classifified and constructed all irreducible kG-module with B-stable line. By the way, we give a new proof of the result of Borel and Tits on the structure of fifinite dimensional irreducible kG-modules.