一个与q盘多项式相关的非交换离散超群
A non-commutative discrete hypergroup associated with q-disk polynomials
摘要：
本文的目的是给出一个与$q$ -圆盘多项式相关的非交换离散超群的例子。这些是多项式$R_{l,m}^{(\a)}$在两个非交换的变量，这是表示通过小$q$ -雅可比多项式，并出现，为值$\a=n-2$，作为带状球面函数的量子模拟的齐性空间$U(n)/U(n-1)$。这是第一次在《易经》中发现的。在文献[1]中，我们证明了这些$q$ -圆盘多项式的一个加法公式.正是这个加法公式，将允许我们以类似于[Koo 1]的方式证明线性化系数的正性，并从它构造一个遵循[Koo 4]的DJS-超群。
英文摘要：
The aim of this paper is to give an example of a non-commutative discrete hypergroup associated with $q$-disk polynomials. These are polynomials $R_{l,m}^{(\a)}$ in two non-commuting variables which are expressed through little $q$-Jacobi polynomials and that appear, for the value $\a=n-2$, as zonal spherical functions on a quantum analogue of the homogeneous space $U(n)/U(n-1)$. This fact was first proved in [NYM] (see also [Fl]). In a previous paper [Fl] we proved an addition formula for these $q$-disk polynomials. It is this addition formula that will allow us to prove positivity of linearization coefficients in a manner similar to [Koo1], and to construct from it a DJS-hypergroup following [Koo4].
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