Modified symmetric polynomials and integrability
Evan Williams Theatre
Peter Hall Building
I will talk about symmetric polynomials from the perspective of integrable lattice models. The examples I will discuss include modified Hall-Littlewood and modified Macdonald polynomials. These polynomials are related to Hall-Littlewood and Macdonald polynomials by a simple basis transformation known as the plethystic substitution. Our approach using lattice models allows us to find several new combinatorial formulas for these polynomials. These formulas include products of certain basic hypergeometric functions for which we find a manifestly positive finite sum expression.
This is a joint work with Michael Wheeler based on the ideas of the work "Matrix product formula for Macdonald polynomials" by Cantini, de Gier and Wheeler.
Dr Alexandr Garbali, University of Melbourne