Interpolation Macdonald polynomials and Cauchy-type identities

NONSYMMETRIC INTERPOLATION MACDONALD POLYNOMIALS AND gln BASIC HYPERGEOMETRIC SERIES

The Knop–Sahi interpolation Macdonald polynomials are inhomogeneous and nonsymmetric generalisations of the well-known Macdonald polynomials. In this paper we apply the interpolation Macdonald polynomials to study a new type of basic hypergeometric series of type gln. Our main results include a new q-binomial theorem, new q-Gauss sum, and several transformation formulae for gln series.

Some conjectures for Macdonald polynomials of type

We present conjectures giving formulas for the Macdonald polynomials of type B, C, D which are indexed by a multiple of the first fundamental weight. The transition matrices between two different types are explicitly given. Introduction Among symmetric functions, the special importance of Schur functions comes from their intimate connection with representation theory. Actually the irreducible p...

Macdonald Polynomials and Geometry

We explain some remarkable connections between the twoparameter symmetric polynomials discovered in 1988 by Macdonald, and the geometry of certain algebraic varieties, notably the Hilbert scheme Hilb(C 2 ) of points in the plane, and the variety Cn of pairs of commuting n× n matrices.

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...

On Cherednik-macdonald–mehta Identities