U_n(q) acting on flags and supercharacters

2014/12/10 by Dipper, Richard, Guo, Qiong
#20C15 #20C33 #20D15 #20D20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1412.3376

Abstract

Let U=U_n(q) be the group of lower unitriangular n × n-matrices with entries in the field \mathbb F_q with q elements for some prime power q and n ∈ \mathbb N. We investigate the restriction to U of the permutation action of GL_n(q) on flags in the natural GL_n(q)-module \mathbb F_qⁿ. 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 \mathbb C U-modules.

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