论文标题
两个二元性：马尔可夫和舒尔·韦尔
Two dualities: Markov and Schur-Weyl
论文作者
论文摘要
我们表明，量子schur-weyl双重性导致多种不对称相互作用粒子系统的马尔可夫二元性。特别是我们考虑三种情况： （1）使用两参数量子组和来自Arxiv的两参数Hecke代数之间的Schur-Weyl二元性：Math/0108038，我们恢复了先前在Arxiv中发现的多种物种ASEP的Markov自偶性：1605.00691和Arxiv和Arxiv：1606.06.045887。 （2）从量子组的共同理想的亚代词和B型a型a型的Hecke代数：1609.01766之间，我们找到了在半偶然线上的多物种开放式ASEP。二元功能以前尚未出现在文献中。 （3）Arxiv：2001.11372的“ Fused” Hecke代数导致了一个新过程，我们称之为编织的ASEP。在编织的ASEP中，最多的M颗粒可能占据位点，最多可在M颗粒中跳跃。这个Hecke代数与量子组之间的二元性二元性导致了马尔可夫二元性。二元函数先前已作为多物种ASEP（Q，M/2）ARXIV的双重性函数：1605.00691和随机多物种较高的自旋顶点模型ARXIV：1701.04468。
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.
