Dr. Nathaniel Thiem
A supercharacter theory of a nite 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 nite eld, that has a rich combinato-rial 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 coe cients that are not well understood in general. This paper constructs a family of modules for Un, and uses these modules to describe the coe cients arising from restrictions of certain supercharacters. This description involves introducing certain q-analog binomial coe cients associated to a nite poset.
Bragg, Daniel, "Restrictions of Rainbow Supercharacters and Poset Binomials" (2013). Undergraduate Honors Theses. 404.