创新团队讨论班系列学术报告

报告人：郭琼（斯图加特大学博士研究生， 表示论）

题目： Standard basis of unipotent Specht modules of finite general linear groups

时间： 2010年 10月 21 日 （周四） 下午 14：30-16：20

地点： 4号教学楼207多媒体教室

摘要：

This is a joint work with B. Ackermann and R. Dipper.

Let p be a prime and q be some prime power. Let G = GLn(q) and U be the subgroup of unipotent lower triangular matrices of G. We determine the precise U-module structure of the unipotent Specht modules of G associated with two part partitions over finite fields of characteristic not dividing q. In previous work, Dipper, James and Lyle have constructed standard basis for these Specht modules, but in a combinational way. Now we give a new interpretation in the way of representation theory of the Specht module. Moreover, we also show how our work relates to a theorem of Isaacs which says, the degrees of the ordinary irreducible epresentations of U are powers of q.