Macdonald functions associated to complex reflection groups

Department of Mathematics, Science University of Tokyo, Noda, Chiba 278-8510, Japan
Journal of Algebra (Impact Factor: 0.6). 02/2003; 260(1):426-448. DOI: 10.1016/S0021-8693(02)00673-7
Source: arXiv


Let W be the complex reflection group . In the author's previous paper [J. Algebra 245 (2001) 650–694], Hall–Littlewood functions associated to W were introduced. In the special case where W is a Weyl group of type Bn, they are closely related to Green polynomials of finite classical groups. In this paper, we introduce a two variables version of the above Hall–Littlewood functions, as a generalization of Macdonald functions associated to symmetric groups. A generalization of Macdonald operators is also constructed, and we characterize such functions by making use of Macdonald operators, assuming a certain conjecture.

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