On monomial linearisation and supercharacters of pattern subgroups

2017/01/03 by Guo, Qiong, Dipper, Richard
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1701.00605

Abstract

Column closed pattern subgroups U of the finite upper unitriangular groups U_n(q) are defined as sets of matrices in U_n(q) having zeros in a prescribed set of columns besides the diagonal ones. We explain Jedlitschky's construction of monomial linearisation and apply this to C U yielding a generalisation of Yan's coadjoint cluster representations. Then we give a complete classification of the resulting supercharacters, by describing the resulting orbits and determining the Hom-spaces between orbit modules.

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