Annals of Combinatorics 3 (1999) 385-415

Symmetric and Nonsymmetric Macdonald Polynomials

Dan Marshall

Department of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3052, Australia

Received December 2, 1998

AMS Subject Classification: 33D80

Abstract. The symmetric Macdonald polynomials may be constructed from the nonsymmetric Macdonald polynomials. This allows us to develop the theory of the symmetric Macdonald polynomials by first developing the theory of their nonsymmetric counterparts. In taking this approach we are able to obtain new results as well as simpler and more accessible derivations of a number of the known fundamental properties of both kinds of polynomials.

Keywords: Macdonald polynomials, q-series, Hecke algebras


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