Title: Specializations of Macdonald polynomials using multiline queues and multiline diagrams
| Speaker: | Jerónimo Valencia |
| Affiliation: | University of Waterloo |
| Location: | MC 5501 |
Abstract: Multiline queues were introduced by Ferrari and Martin to model the stationary states of the TASEP, a 1D non-equilibrium particle model. Later, Corteel, Mandelshtam, and Williams gave a formula for the Macdonald polynomial using a (X,q,t)-weighted version of multiline queues. This talk aims to develop the combinatorics of such objects in the t=0 case. We introduce an insertion algorithm on multiline queues that leads to new proofs of the charge expansion of q--Whittaker polynomials in the Schur basis, the Littlewood--Richardson rule and the Cauchy identity for binary matrices. We generalize these ideas to multiline diagrams, a plethystic analog of multiline queues, yielding a cocharge formula for the modified Hall--Littlewood polynomials and another proof of the second Cauchy identity for integer matrices. This is joint work with Olya Mandelshtam.