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arXiv · 1506.04490

Multispecies TASEP and combinatorial $R$

Atsuo Kuniba·Shouya Maruyama·Masato Okado
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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 $q=0$.

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Atsuo Kuniba, Shouya Maruyama, Masato Okado. 2015-06-15. Multispecies TASEP and combinatorial $R$. https://doi.org/10.1088/1751-8113/48/34/34ft02

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