Restrictions of Rainbow Supercharacters and Poset Binomials
نویسندگان
چکیده
A supercharacter theory of a finite group is a natural approximation to the ordinary character theory. There is a particularly nice supercharacter theory for Un, the group of unipotent upper triangular matrices over a finite field, that has a rich combinatorial structure based on set partitions. Various representation theoretic constructions such as restriction and induction have supercharacter theoretic analogues. In the case of Un, restrictions give rise to families of coefficients that are not well understood in general. This paper constructs a family of modules for Un, and uses these modules to describe the coefficients arising from restrictions of certain supercharacters. This description involves introducing certain q-analog binomial coefficients associated to a finite poset. RESTRICTIONS OF RAINBOW SUPERCHARACTERS AND POSET BINOMIALS 1
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