On unitriangular decomposition matrices

发布时间：2023-10-16 作者：浏览次数：

Speaker:	冯致程	DateTime:	2023年10月20日（周五）下午14:30-16:30
Brief Introduction to Speaker: 冯致程，2017年博士毕业于北京大学，2017-2022年先后在TU Kaiserslautern、北京科技大学工作。2022年加入南方科技大学，现任助理教授。主要研究领域为群及其表示，特别是局部–整体问题和Lie型群的表示。		Place:	6号楼2楼报告厅
Abstract:Irreducible representations of finite groups over fields of positive characteristic, or equivalently irreducible Brauer characters, make a quite difficult subject. Most of the problems and results can be studied via the decomposition matrix relating the set of irreducible Brauer characters to the better understood set of ordinary characters. Many decomposition matrices of finite groups enjoy the property of unitriangularity. We establish a going-up property showing that basic sets and unitriangularity transfer to an overgroups and focus on the finite reductive groups in non-defining characteristic. Jordan decomposition helps applying that to some conjectures on representations of finite groups. Joint work with Britta Späth.