Cherednik algebras, Macdonald polynomials and combinatorics

• Autores: Mark D. Haiman
• Localización: Proceedings oh the International Congress of Mathematicians: Madrid, August 22-30,2006 : invited lectures / coord. por Marta Sanz Solé , Javier Soria de Diego , Juan Luis Varona Malumbres , Joan Verdera , Vol. 3, 2006, ISBN 978-3-03719-022-7, págs. 843-872
• Idioma: inglés
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• Resumen

  • 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.