Characters of the rook monoid

Algebraic and Enumerative Combinatorics Seminar

Abstract:

The partial permutations form a monoid known in different contexts as either the “symmetric inverse semigroup” or the “rook monoid.” In this talk I will define a family of symmetric functions that evaluate to the character values of the irreducible representations of the monoid. The basis also connects to the representation theory of the Schur-Weyl duality with the “propagating partition algebra.” Moreover, the structure coefficients of this basis interpolate between the Kronecker coefficients and the Littlewood-Richardson coefficients and we use it to develop some of the combinatorics of the connection.

This is joint work with Rosa Orellana and Alex Wilson.

There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.