Cherednik algebras, Macdonald polynomials and combinatorics

  • Mark Haiman

    University of California, Berkeley, USA
Cherednik algebras, Macdonald polynomials and combinatorics cover
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Abstract

In the first part of this article we review the general theory of Cherednik algebras and non-symmetric Macdonald polynomials, including a formulation and proof of the fundamental duality theorem in its proper general context. In the last section we summarize some of the combinatorial results in this area which we have recently obtained in collaboration with J. Haglund and N. Loehr.