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| Title: | Unitary representations of affine Hecke algebras related to Macdonald spherical functions |
| Authors: | van Diejen, J.F.
Emsiz, E. |
| Keywords: | Symmetric functions
Affine Hecke algebras
Spherical functions |
| Issue Date: | Mar-2012 |
| Publisher: | ACADEMIC PRESS INC ELSEVIER SCIENCE, 525 B ST, STE 1900, SAN DIEGO, CA 92101-4495 USA |
| Citation: | JOURNAL OF ALGEBRA Volume: 354 Issue: 1 Pages: 180-210 DOI: 10.1016/j.jalgebra.2012.01.005 |
| Abstract: | For any reduced crystallographic root system, we introduce a unitary representation of the (extended) affine Hecke algebra given by discrete difference-reflection operators acting in a Hilbert space of complex functions on the weight lattice. It is shown that the action of the center under this representation is diagonal on the basis of Macdonald spherical functions. As an application, we compute an explicit Pieri formula for these spherical functions. (C) 2012 Elsevier Inc. All rights reserved. |
| URI: | http://dspace.utalca.cl/handle/1950/9082 |
| ISSN: | 0021-8693 |
| Appears in Collections: | Artículos en publicaciones ISI - Universidad de Talca
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