Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra
This paper builds on the previous paper by the author, where a relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra (DAHA) corresponding to the Askey-Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to AW(...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2008 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2008
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149029 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra / T.H. Koornwinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862542319409954816 |
|---|---|
| author | Koornwinder, T.H. |
| author_facet | Koornwinder, T.H. |
| citation_txt | Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra / T.H. Koornwinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper builds on the previous paper by the author, where a relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra (DAHA) corresponding to the Askey-Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to AW(3) with an additional relation that the Casimir operator equals an explicit constant. A similar result with q-shifted parameters holds for the antispherical subalgebra. Some theorems on centralizers and centers for the algebras under consideration will finally be proved as corollaries of the characterization of the spherical and antispherical subalgebra.
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| first_indexed | 2025-11-24T18:45:31Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149029 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T18:45:31Z |
| publishDate | 2008 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Koornwinder, T.H. 2019-02-19T13:09:25Z 2019-02-19T13:09:25Z 2008 Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra / T.H. Koornwinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 15 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 33D80 https://nasplib.isofts.kiev.ua/handle/123456789/149029 This paper builds on the previous paper by the author, where a relationship between Zhedanov's algebra AW(3) and the double affine Hecke algebra (DAHA) corresponding to the Askey-Wilson polynomials was established. It is shown here that the spherical subalgebra of this DAHA is isomorphic to AW(3) with an additional relation that the Casimir operator equals an explicit constant. A similar result with q-shifted parameters holds for the antispherical subalgebra. Some theorems on centralizers and centers for the algebras under consideration will finally be proved as corollaries of the characterization of the spherical and antispherical subalgebra. This paper is a contribution to the Proceedings of the Seventh International Conference “Symmetry in Nonlinear Mathematical Physics” (June 24–30, 2007, Kyiv, Ukraine). I thank Jasper Stokman for suggesting me that the spherical subalgebra of the Askey–Wilson DAHA is related to Zhedanov’s algebra. I thank a referee for suggestions which led to inclusion of Remarks 2.1, 2.7 and 4.5. Some of the results presented here were obtained during the workshop Applications of Macdonald Polynomials, September 9–14, 2007 at the Banf f International Research Station (BIRS). I thank the organizers for inviting me. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra Article published earlier |
| spellingShingle | Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra Koornwinder, T.H. |
| title | Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra |
| title_full | Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra |
| title_fullStr | Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra |
| title_full_unstemmed | Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra |
| title_short | Zhedanov's Algebra AW(3) and the Double Affine Hecke Algebra in the Rank One Case. II. The Spherical Subalgebra |
| title_sort | zhedanov's algebra aw(3) and the double affine hecke algebra in the rank one case. ii. the spherical subalgebra |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149029 |
| work_keys_str_mv | AT koornwinderth zhedanovsalgebraaw3andthedoubleaffineheckealgebraintherankonecaseiithesphericalsubalgebra |