论文标题
等级的表示两个RACAH代数和正交多元多项式
Representations of the rank two Racah algebra and orthogonal multivariate polynomials
论文作者
论文摘要
详细研究了等级两个RACAH代数的代数结构。我们提供该代数的自动形态组，这是五个元素的排列组的同构。该组可以用几何解释为折叠的Icosidodecahedron的对称性。它使我们能够研究此RACAH代数的一类等效表现。可以对称它们对称，以使它们的过渡矩阵正交。我们证明他们的条目可以用RACAH多项式表示。这种构建提供了替代证明Tratnik多项式满足的复发，差异和正交关系，及其作为两个单向RACAH多项式的产物的表达方式。我们的构造提供了这些双变量多项式的概括及其性能。
The algebraic structure of the rank two Racah algebra is studied in detail. We provide an automorphism group of this algebra, which is isomorphic to the permutation group of five elements. This group can be geometrically interpreted as the symmetry of a folded icosidodecahedron. It allows us to study a class of equivalent irreducible representations of this Racah algebra. They can be chosen symmetric so that their transition matrices are orthogonal. We show that their entries can be expressed in terms of Racah polynomials. This construction gives an alternative proof of the recurrence, difference and orthogonal relations satisfied by the Tratnik polynomials, as well as their expressions as a product of two monovariate Racah polynomials. Our construction provides a generalization of these bivariate polynomials together with their properties.
