Tuesday, August 27, 14:00, 7.527

Qiong Guo (Shanghai Institute of Technology), Supercharacters of row and column closed pattern subgroups of finite unitriangular groups, I.

Abstract:
The supercharacter theory was first introduced by André and Yan for Un(q), the upper unitriangular groups, and then generalized by Diaconis and Isaacs to Fq-algebra groups. This talk will focus on some special pattern subgroups UJ of Un(q), which we called row and column closed pattern subgroups. In this talk, we shall introduce a monomial basis for CUJ and show that the orbit modules generated by this monomial basis are either disjoint or isomorphic. In particular, the characters afforded by these orbit modules are exactly supercharacters of UJ. Moreover, we give the representatives for each right orbit modules generated by the monomial basis.
This is a joint work with Richard Dipper.