{
  "id": "2209.03531",
  "version": "v1",
  "published": "2022-09-08T02:14:10.000Z",
  "updated": "2022-09-08T02:14:10.000Z",
  "title": "Orthogonal polynomial duality and unitary symmetries of multi--species ASEP$(q,\\boldsymbolθ)$ and higher--spin vertex models via $^*$--bialgebra structure of higher rank quantum groups",
  "authors": [
    "Chiara Franceschini",
    "Jeffrey Kuan",
    "Zhengye Zhou"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We propose a novel, general method to produce orthogonal polynomial dualities from the $^*$--bialgebra structure of Drinfeld--Jimbo quantum groups. The $^*$--structure allows for the construction certain \\textit{unitary} symmetries, which imply the orthogonality of the duality functions. In the case of the quantum group $\\mathcal{U}_q(\\mathfrak{gl}_{n+1})$, the result is a nested multivariate $q$--Krawtchouk duality for the $n$--species ASEP$(q,\\boldsymbol{\\theta})$. The method also applies to other quantized simple Lie algebras and to stochastic vertex models",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-08T02:14:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "higher rank quantum groups",
      "orthogonal polynomial duality",
      "higher-spin vertex models",
      "bialgebra structure",
      "multi-species asep"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}