On monomial linearisation and supercharacters of pattern subgroups

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 $CU$ 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.

accepted for publication in SCIENCE CHINA Mathematics

References in corpus (1)

• Representations of Finite Unipotent Linear Groups by the Method of Clusters