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arXiv · 1701.00605

On monomial linearisation and supercharacters of pattern subgroups

Qiong Guo·Richard Dipper
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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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Qiong Guo, Richard Dipper. 2017-01-03. On monomial linearisation and supercharacters of pattern subgroups. https://arxiv.org/abs/1701.00605

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