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Macdonald functions associated to complex reflection groups

✍ Scribed by Toshiaki Shoji

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
218 KB
Volume
260
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let W be the complex reflection group S n (Z/eZ) n . 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 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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