NONSYMMETRIC INTERPOLATION MACDONALD POLYNOMIALS AND gln BASIC HYPERGEOMETRIC SERIES
نویسنده
چکیده
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.
منابع مشابه
Yangian Gelfand-Zetlin Bases, glN-Jack Polynomials and computation of Dynamical Correlation Functions in the Spin Calogero-Sutherland Model
We consider the glN -invariant Calogero-Sutherland Models with N = 1, 2, 3, . . . in a unified framework, which is the framework of Symmetric Polynomials. By the framework we mean an isomorphism between the space of states of the glN -invariant Calogero-Sutherland Model and the space of Symmetric Laurent Polynomials. In this framework it becomes apparent that all the glN -invariant Calogero-Sut...
متن کاملDouble Affine Hecke Algebras and Difference Fourier Transforms
0. Introduction 1. Affine Weyl groups (Reduction modulo W ) 2. Double Hecke algebras (Automorphisms, Demazure-Lusztig operators) 3. Macdonald polynomials (Intertwining operators) 4. Fourier transform on polynomials (Basic transforms) 5. Jackson integrals (Macdonald’s η-identities) 6. Semisimple representations (Main Theorem, GLn and other applications) 7. Spherical representations (Semisimple s...
متن کاملIntegrality of Two Variable Kostka Functions
Macdonald defined in [M1] a remarkable class of symmetric polynomials Pλ(x; q, t) which depend on two parameters and interpolate between many families of classical symmetric polynomials. For example Pλ(x; t) = Pλ(x; 0, t) are the Hall-Littlewood polynomials which themselves specialize for t = 0 to Schur functions sλ. Also Jack polynomials arise by taking q = t and letting t tend to 1. The Hall-...
متن کاملA representation-theoretic proof of the branching rule for Macdonald polynomials
We give a new representation-theoretic proof of the branching rule for Macdonald polynomials using the Etingof-Kirillov Jr. expression for Macdonald polynomials as traces of intertwiners of Uq(gln). In the GelfandTsetlin basis, we show that diagonal matrix elements of such intertwiners are given by application of Macdonald’s operators to a simple kernel. An essential ingredient in the proof is ...
متن کاملSome Conjectures for Macdonald Polynomials of Type B, C, D
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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008