In the second talk, we will explore the combinatorics of set-partitions via a supercharacter theory of the group of finite unipotent upper-triangular matrices. This classical example was the original motivation for defining supercharacters, and the resulting combinatorics is analogous to the integer partitions in the representation theory of the symmetric group. By studying the decomposition of restrictions and tensor products of supercharacters into supercharacters, this talk finds a surprising analogue to the combinatorics of the Littlewood--Richardson coefficients of the symmetric group. Joint with S. Lewis.
Supercharacters and the combinatorics of set-partitions II
Supercharacters and the combinatorics of set-partitions II