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періодичних видань НАН України
The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case
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- Symmetry, Integrability and Geometry: Methods and Applications, 2007, том 3
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| dc.contributor.author | Koornwinder, T.H. | |
| dc.date.accessioned | 2019-02-14T14:53:30Z | |
| dc.date.available | 2019-02-14T14:53:30Z | |
| dc.date.issued | 2007 | |
| dc.identifier.citation | The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case / T.H. Koornwinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 16 назв. — англ. | uk_UA |
| dc.identifier.issn | 1815-0659 | |
| dc.identifier.other | 2000 Mathematics Subject Classification: 33D80; 33D45 | |
| dc.identifier.uri | http://dspace.nbuv.gov.ua/handle/123456789/147378 | |
| dc.description.abstract | Zhedanov's algebra AW(3) is considered with explicit structure constants such that, in the basic representation, the first generator becomes the second order q-difference operator for the Askey-Wilson polynomials. It is proved that this representation is faithful for a certain quotient of AW(3) such that the Casimir operator is equal to a special constant. Some explicit aspects of the double affine Hecke algebra (DAHA) related to symmetric and non-symmetric Askey-Wilson polynomials are presented and proved without requiring knowledge of general DAHA theory. Finally a central extension of this quotient of AW(3) is introduced which can be embedded in the DAHA by means of the faithful basic representations of both algebras. | uk_UA |
| dc.description.sponsorship | This paper is a contribution to the Vadim Kuznetsov Memorial Issue ‘Integrable Systems and Related Topics’. I am very much indebted to an anonymous referee who pointed out errors in the proof of an earlier version of Theorem 2.2. I also thank him for suggesting a further simplification in my proof of the corrected theorem. I thank Siddhartha Sahi for making available to me a draft of his paper in an early stage. I also thank Jasper Stokman for helpful comments. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Інститут математики НАН України | uk_UA |
| dc.relation.ispartof | Symmetry, Integrability and Geometry: Methods and Applications | |
| dc.title | The Relationship between Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case | uk_UA |
| dc.type | Article | uk_UA |
| dc.status | published earlier | uk_UA |
