Integrable Structure of Multispecies Zero Range Process

Abstract

We present a brief review on integrability of multispecies zero range process in one dimension introduced recently. The topics range over stochastic $R$ matrices of quantum affine algebra $U_q(A_n^{(1)})$, matrix product construction of stationary states for periodic systems, $q$-boson representation of Zamolodchikov-Faddeev algebra, etc. We also introduce new commuting Markov transfer matrices having a mixed boundary condition and prove the factorization of a family of $R$ matrices associated with the tetrahedron equation and generalized quantum groups at a special point of the spectral parameter.

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Cited by in corpus (2)

• Modified Macdonald polynomials and the multispecies zero range process: I
• New formulas for Macdonald polynomials via the multispecies exclusion and zero range processes