Séminaire Lotharingien de Combinatoire, 85B.56 (2021), 12 pp.
Arvind Ayyer, Olya Mandelshtam and James Martin
Multispecies TAZRP and Modified Macdonald Polynomials
Abstract.
Recently, a formula for the symmetric Macdonald polynomials Pλ(X;q,t) was given in terms of objects called multiline queues, which also compute probabilities of a statistical mechanics model called the multispecies ASEP on a ring.
It is natural to ask whether the modified Macdonald polynomials H˜λ(X;q,t) can be obtained using a combinatorial gadget for some other
statistical mechanics model. We answer this question in the affirmative. In this article, we give a new formula for H˜λ(X;q,t) in terms of fillings of tableaux called polyqueue tableaux. We define a multispecies TAZRP on a ring with parameter t, whose (unnormalized) stationary probabilities are computed by polyqueue tableaux, and whose partition function is equal to
H˜λ(X;1,t).
Received: December 1, 2020.
Accepted: March 1, 2021.
Final version: April 29, 2021.
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