Title: Factorial Schur Functions and Quantum Intergrability
|Affiliation:||University of Waterloo|
|Zoom:||Contact Karen Yeats|
I will introduce factorial Schur functions as they relate to my Master's thesis. Factorial Shur functions are a generalization of Schur functions with a second family of "shift" parameters. In 2009, Zinn-Justin reproved the answer to a tiling problem (the puzzle rule) with a toy fermionic model, using techniques from physics to extract the result. He showed the same tiles can be arranged to represent factorial Schur functions. The same facts can then be used to prove a Littlewood-Richardson rule for factorial Schur functions with the same first set of variables. I will go over the ideas of this proof and get into results that have built on top of this theory. For example, a Littlewood-Richardson rule for Grothendieck polynomials can be shown in a similar way.