Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0859.17005
Etingof, Pavel I.; Kirillov, Alexander A.jun.
Representation-theoretic proof of the inner product and symmetry identities for Macdonald's polynomials. (English)
[J] Compos. Math. 102, No.2, 179-202 (1996). ISSN 0010-437X; ISSN 1570-5846/e

In 1988 {\it I. G. Macdonald} introduced a new class of symmetric polynomials in Publ. I.R.M.A. Strasbourg, 372/S-20, Actes 20 Séminaire Lotharingien, 131-171 (1988). In a previous paper the authors of the work under review obtained those Macdonald's polynomials related to the root system $A_{n-1}$ via finite-dimensional representation of the quantum group $U_q{\germ{sl}}_n$. Here they give a representation-theoretic proof of Macdonald's inner product and symmetry identities in the $A_{n-1}$-case. Previously, analogous results had been obtained by combinatorial methods by Macdonald and, in the more general case, by Cherednik. The proof uses intertwining operators and Shapovalov's formula as well as the ribbon graphs of Reshetikhin and Turaev.
[Stefano Capparelli (Roma)]

MSC 2000:: *17B37 Quantum groups and related deformations
05E05 Symmetric functions

Keywords: quantum groups; Macdonald's polynomials; symmetry identities

Cited in: Zbl 0932.33028

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]