论文标题
双变量连续的Q-热线多项式和变形的量子关系
Bivariate Continuous q-Hermite Polynomials and Deformed Quantum Serre Relations
论文作者
论文摘要
我们引入了连续Q-热线多项式的双变量版本。我们为它们获得代数属性（生成函数，根据单变量的表达式，向后差方程和复发关系）和分析属性（确定正交性测量）。我们发现双变量连续的Q-热线多项式与[Kolb和Yakimov，Adv。数学。 2020]用于量子对称对，以建立用于kac-moody类型的准切片量子对称对的变形量子关系。我们证明，这些定义关系是通过通过多元正交多项式替换所有单一元素来从通常的量子serre关系中获得的。
We introduce bivariate versions of the continuous q-Hermite polynomials. We obtain algebraic properties for them (generating function, explicit expressions in terms of the univariate ones, backward difference equations and recurrence relations) and analytic properties (determining the orthogonality measure). We find a direct link between bivariate continuous q-Hermite polynomials and the star product method of [Kolb and Yakimov, Adv. Math. 2020] for quantum symmetric pairs to establish deformed quantum Serre relations for quasi-split quantum symmetric pairs of Kac-Moody type. We prove that these defining relations are obtained from the usual quantum Serre relations by replacing all monomials by multivariate orthogonal polynomials.
