Algebraic combinatorics seminar - Yan Xu

A Bernstein Creation Operator of Schur Basis

Abstract:

In this talk, I will introduce an operator B that acts on 1 to create the Schur basis of Sym. To construct this operator, we will need to consider elementary basis indexed by an integer r as an operator that adds vertical strip of size r on a diagram of an integer partition over all possible ways. From this we can define the dual operator of elementary operator. Go through some construction of commutation of those operator and generation functions of those operator we will find Schur basis is the coefficient of certain term of the generating function B(z). This talk only requires a little background of symmetric functions.