论文标题
多物种ASEP $（Q，\boldsymbolθ）$和高级式顶点模型的多种物种ASEP $（Q，\boldsymbolθ）的正交多项式双重性和统一对称性通过$^*$ - 较高等级量子组的bialgebra结构
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
论文作者
论文摘要
我们提出了一种新颖的一般方法，以从$^*$ - 吉姆博量子组的$^*$ - bialgebra结构中产生正交多项式双重性。 $^*$ - 结构允许构建某些\ textit {unital}对称性，这意味着双重性功能的正交性。对于量子组$ \ MATHCAL {U} _Q（\ Mathfrak {gl} _ {n+1}）$，结果是嵌套的多变量$ q $ - krawtchouk duality for $ n $ - 物种ASEP $（q，\boldsymbolθ）$。该方法还适用于其他量化的简单谎言代数和随机顶点模型。 作为二元性关系的概率应用，我们为两种特征$ q $ -tazrp（完全不对称的零范围过程）提供了$ q- $ chirted阶乘时刻的明确公式（即pochhammer符号的$ q $ -Analogue）。
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 of 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$(q,\boldsymbolθ)$. The method also applies to other quantized simple Lie algebras and to stochastic vertex models. As a probabilistic application of the duality relation found, we provide the explicit formula of the $q-$shifted factorial moments (namely the $q$-analogue of the Pochhammer symbol) for the two--species $q$--TAZRP (totally asymmetric zero range process).
