Date and time: 11th October 2022, 2.30 to 3.30 pm
Title: A multispecies totally asymmetric zero range process and Macdonald polynomials
Abstract: Macdonald polynomials are a remarkable family of symmetric functions that are known to have connections to combinatorics, algebraic geometry and representation theory. Due to work of Corteel, Mandelshtam and Williams, it is known that they are related to the asymmetric simple exclusion process (ASEP) on a ring.
The modified Macdonald polynomials are obtained from the Macdonald polynomials using an operation called plethysm. It is natural to ask whether the modified Macdonald polynomials are related to some other particle system. In this talk, we answer this question in the affirmative via a multispecies totally asymmetric zero-range process (TAZRP). We also present a Markov process on tableaux that projects to the TAZRP and derive formulas for stationary probabilities and certain correlations. We also prove a remarkable symmetry property for local correlations.