Un(q) acting on flags and supercharacters

作者：Dipper, Richard^*; Guo, Qiong^*

来源：Journal of Algebra, 2017, 475: 80-112.

DOI：10.1016/j.jalgebra.2016.07.014

• Flags
• Monomial linearization
• Supercharacter

Let U = U-n(q) be the group of lower unitriangular n x n-matrices with entries in the field F-q with q elements for some prime power q and n is an element of N. We investigate the restriction to U of the permutation action of GL(n)(q) on flags in the natural GL(n)(q)-module F-q(n). Applying our results to the special case of flags of length two we obtain a complete decomposition of the permutation representation of GL(n)(q) on the cosets of maximal parabolic subgroups into irreducible CU-modules.

• 出版日期2017-4-1
• 单位上海应用技术大学