Bisymmetric functions, Macdonald polynomials and basic hypergeometric series
نویسندگان
چکیده
منابع مشابه
Bisymmetric functions, Macdonald polynomials and sl3 basic hypergeometric series
A new type of sl3 basic hypergeometric series based on Macdonald polynomials is introduced. Besides a pair of Macdonald polynomials attached to two different sets of variables, a key-ingredient in the sl3 basic hypergeometric series is a bisymmetric function related to Macdonald’s commuting family of q-difference operators, to the sl3 Selberg integrals of Tarasov and Varchenko, and to alternati...
متن کاملMacdonald Polynomials and Multivariable Basic Hypergeometric Series
Abstract. We study Macdonald polynomials from a basic hypergeometric series point of view. In particular, we show that the Pieri formula for Macdonald polynomials and its recently discovered inverse, a recursion formula for Macdonald polynomials, both represent multivariable extensions of the terminating very-well-poised 6φ5 summation formula. We derive several new related identities including ...
متن کاملNONSYMMETRIC 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.
متن کاملq-Hypergeometric Series and Macdonald Functions
Abstract We derive a duality formula for two-row Macdonald functions by studying their relation with basic hypergeometric functions. We introduce two parameter vertex operators to construct a family of symmetric functions generalizing Hall-Littlewood functions. Their relation with Macdonald functions is governed by a very well-poised q-hypergeometric functions of type 4 0$, for which we obtain ...
متن کاملBRANCHING RULES FOR SYMMETRIC MACDONALD POLYNOMIALS AND sln BASIC HYPERGEOMETRIC SERIES
Abstract. A one-parameter generalisation Rλ(X; b) of the symmetric Macdonald polynomials and interpolations Macdonald polynomials is studied from the point of view of branching rules. We establish a Pieri formula, evaluation symmetry, principal specialisation formula and q-difference equation for Rλ(X; b). We also prove a new multiple q-Gauss summation formula and several further results for sl...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Compositio Mathematica
سال: 2008
ISSN: 0010-437X,1570-5846
DOI: 10.1112/s0010437x07003211