Generalized Cherednik-Macdonald identities

On Cherednik-macdonald–mehta Identities

On Cherednik–macdonald–mehta Identities

In this note we give a proof of Cherednik’s generalization of Macdonald–Mehta identities for the root system An−1, using representation theory of quantum groups. These identities give an explicit formula for the integral of a product of Macdonald polynomials with respect to a “difference analogue of the Gaussian measure”. They were suggested by Cherednik, who also gave a proof based on represen...

Some Constant Term Identities of Cherednik-macdonald-mehta Type

We study t-analogs of string functions for integrable highest weight representations of the affine Kac-Moody algebra A (1) 1 . We obtain closed form formulas for certain t-string functions of levels 2 and 4. As corollaries, we obtain explicit identities for the corresponding affine Hall-Littlewood functions, as well as higher-level generalizations of Cherednik’s Macdonald and Macdonald-Mehta co...

Cherednik algebras, Macdonald polynomi- als and combinatorics

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. Mathematics ...

Universal Characters from the Macdonald Identities

The main result of [Kos] shows that a sequence of complexes associated with the MacDonald identities gives a sequence of universal characters which extends and generalises some representations of the exceptional series given in [Del96]. This proves the conjectures in [MP03]. In this paper we use a twisted version of this definition to define a sequence of complexes for the first row of the Freu...