Macdonald functions associated to complex reflection groups

Details Macdonald functions associated to complex reflection groups Macdonald functions associated to complex reflection groups

2002-08-08

arxiv.org/abs/math/0208061v1

Mathematics

Quantum Algebra

22 pages

Scientific paper

Let W be the complex reflection group G(e,1,n). In the author's previous paper, Hall-Littlewood functions associated to W were introduced. In the special case where W is a Weyl group of type B_n, 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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