DMCA
Representation-Theoretic Proof Of The Inner Product And Symmetry Identities For Macdonald's Polynomials (1996)
| Venue: | Compositio Math |
| Citations: | 12 - 1 self |
BibTeX
@ARTICLE{Etingof96representation-theoreticproof,
author = {Pavel I. Etingof and Alexander A. Kirillov and Jr.},
title = {Representation-Theoretic Proof Of The Inner Product And Symmetry Identities For Macdonald's Polynomials},
journal = {Compositio Math},
year = {1996},
volume = {102},
pages = {179--202}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
This paper is a continuation of our papers [EK1, EK2]. In [EK2] we showed that for the root system An\Gamma1 one can obtain Macdonald's polynomials -- a new interesting class of symmetric functions recently defined by I. Macdonald [M1] -- as weighted traces of intertwining operators between certain finite-dimensional representations of U q sl n . The main goal of the present paper is to use this construction to give a representation-theoretic proof of Macdonald's inner product and symmetry identities for the root system An\Gamma1 . Macdonald's inner product identities (see [M2]) have been proved by combinatorial methods by Macdonald (unpublished) for the root system An\Gamma1 and by Cherednik in the general case; symmetry identities for the root system An\Gamma1 have also been proved by Macdonald ([Macdonald, private communication]). The paper is organized as follows. In Section 1 we briefly list the basic definitions. In Section 2 we define Macdonald's polynomials P and recall the construction of
Keyphrases
symmetry identity representation-theoretic proof root system inner product symmetric function basic definition combinatorial method weighted trace inner product identity private communication general case main goal new interesting class macdonald m1 present paper certain finite-dimensional representation
