Title: Bijective Proofs with Tableaux

Abstract:
Bijective proofs involving Young tableaux can provide insight into the combinatorial structure of symmetric functions, but some algebraic constructions are difficult to model combinatorially. In particular, vertex operators and creation operators are two such algebraic tools. In this talk, I will discuss an approach to studying these operators combinatorially through explicit bijections between Young tableaux. I will show how a sign-reversing involution can be used to construct the Schur functions. Time permitting, I will discuss progress towards extending this approach to other families of functions, such as the Hall-Littlewood functions and Macdonald polynomials.