Polynomials Associated with Dihedral Groups

被引：7

作者：

Dunkl, Charles F. ^{[1
]}

机构：

[1] Univ Virginia, Dept Math, Charlottesville, VA 22904 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2007年 / 3卷

关键词：

intertwining operator; Jacobi polynomials;

D O I：

10.3842/SIGMA.2007.052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

There is a commutative algebra of differential-difference operators, with two parameters, associated to any dihedral group with an even number of reflections. The intertwining operator relates this algebra to the algebra of partial derivatives. This paper presents an explicit form of the action of the intertwining operator on polynomials by use of harmonic and Jacobi polynomials. The last section of the paper deals with parameter values for which the formulae have singularities.

引用

页数：19

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