• DOI:10.1093/IMRN/RNAA333
• Corpus ID: 220041604

Two Dualities: Markov and Schur–Weyl

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

• Jeffrey Kuan
• Published 24 June 2020
• Mathematics
• arXiv: Probability

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 Hecke algebra of type B arXiv:1609.01766, we find a Markov duality for a multi-species open ASEP on the semi-infinite line. The duality functional has not previously appeared in the literature.
(3) A "fused" Hecke algebra from arXiv:2001.11372 leads to a new process, which we call braided ASEP. In braided ASEP, up to m particles may occupy a site and up to m particles may jump at a time. The Schur-Weyl duality between this Hecke algebra and a quantum group lead to a Markov duality. The duality function had previously appeared as the duality function of the multi-species ASEP(q,m/2) arXiv:1605.00691 and the stochastic multi-species higher spin vertex model arXiv:1701.04468.