# Two Dualities: Markov and Schur–Weyl

@article{Kuan2020TwoDM, title={Two Dualities: Markov and Schur–Weyl}, author={Jeffrey Kuan}, journal={arXiv: Probability}, year={2020} }

We show that quantum Schur-Weyl duality leads to Markov duality for a variety of asymmetric interacting particle systems. In particular, we consider three cases:
(1) Using a Schur-Weyl duality between a two-parameter quantum group and a two-parameter Hecke algebra from arXiv:math/0108038, we recover the Markov self-duality of multi-species ASEP previously discovered in arXiv:1605.00691 and arXiv:1606.04587.
(2) From a Schur-Weyl duality between a co-ideal subalgebra of a quantum group and a…

## 3 Citations

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We present in this paper the algebra of fused permutations and its deformation the fused Hecke algebra. The first one is defined on a set of combinatorial objects that we call fused permutations, and…

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We study a class of interacting particle systems with asymmetric interaction showing a self-duality property. The class includes the ASEP(q, θ), asymmetric exclusion process, with a repulsive…

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Baxterisation is a procedure which constructs solutions of the Yang–Baxter equation from algebra representations. A recent paper [Cd20b] provides Baxterisation formulas for a fused Hecke algebra. In…

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