Premium
Macdonald difference operators and Harish‐Chandra series
Author(s) -
Letzter Gail,
Stokman Jasper V.
Publication year - 2008
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/pdm055
Subject(s) - mathematics , centralizer and normalizer , isomorphism (crystallography) , algebra over a field , pure mathematics , series (stratigraphy) , weyl algebra , operator (biology) , hypergeometric function , invariant (physics) , weyl group , mathematical physics , paleontology , biochemistry , chemistry , repressor , gene , transcription factor , crystal structure , biology , crystallography
We analyse the centralizer of the Macdonald difference operator in an appropriate algebra of Weyl group invariant difference operators. We show that it coincides with Cherednik's commuting algebra of difference operators via an analog of the Harish‐Chandra isomorphism. Analogs of Harish‐Chandra series are defined and realized as solutions to the system of basic hypergeometric difference equations associated to the centralizer algebra. These Harish‐Chandra series are then related to both Macdonald polynomials and Chalykh's Baker–Akhiezer functions.