Multispecies TASEP and combinatorial $R$

Abstract

We identify the algorithm for constructing steady states of the $n$-species totally asymmetric simple exclusion process (TASEP) on $L$ site periodic chain by Ferrari and Martin with a composition of combinatorial $R$ for the quantum affine algebra $U_q({\widehat{sl}}_L)$ in crystal base theory. Based on this connection and the factorized form of the $R$ matrix derived recently from the tetrahedron equation, we establish a new matrix product formula for the steady state of the TASEP which is expressed in terms of corner transfer matrices of the $q$-oscillator valued five-vertex model at $q=0$.

16 pages, minor corrections

References in corpus (4)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Matrix representation of the stationary measure for the multispecies TASEP
• Spectrum in multi-species asymmetric simple exclusion process on a ring
• Multispecies TASEP and the tetrahedron equation

Cited by in corpus (16)

• Multispecies TASEP and the tetrahedron equation
• Exact solution to integrable open multi-species SSEP and macroscopic fluctuation theory
• Colored five-vertex models and Lascoux polynomials and atoms
• Matrix product solution to a 2-species TASEP with open integrable boundaries
• Double Grothendieck polynomials and colored lattice models
• Combinatorial mappings of exclusion processes
• Multispecies totally asymmetric zero range process: I. Multiline process and combinatorial $R$
• Inhomogeneous generalization of multispecies totally asymmetric zero range process
• Multiline queues with spectral parameters
• Matrix product construction for Koornwinder polynomials and fluctuations of the current in the open ASEP
• Inhomogenous Multispecies TASEP on a ring with spectral parameters
• Multi species asymmetric simple exclusion process with impurity activated flips
• Tetrahedron equation and Schur functions
• Quasi-solvable lattice models for ${\mathrm{Sp}}_{2n}$ and ${\mathrm{SO}}_{2n+1}$ Demazure atoms and characters
• Multispecies totally asymmetric zero range process: II. Hat relation and tetrahedron equation
• Twisted multiline queues for the steady states of TASEP and TAZRP