Tutte Colloquium - Mike Zabrocki

Title: Symmetric group characters as symmetric functions

Abstract:

The irreducible polynomial representations have Schur polynomials as characters. Similarly there is an in-homogeneous basis of symmetric functions that we call the "irreducible character basis" which are characters of irreducible symmetric group modules when the symmetric group is represented as the subgroup of permutation matrices. Just as the structure coefficients of the Schur functions are known as the Littlewood-Richardson coefficients, the structure coefficients of the irreducible character basis are the reduced Kronecker coefficients. This talk will cover
the history and some combinatorial results.
This is joint work with Rosa Orellana.