Double Affine Hecke Algebras of Rank 1 and the Z₃-Symmetric Askey-Wilson Relations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Double Affine Hecke Algebras of Rank 1 and the Z₃-Symmetric Askey-Wilson Relations
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| Creator |
Ito, T.
Terwilliger, P. |
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| Description |
We consider the double affine Hecke algebra H=H(k₀,k₁,k₀v,k₁v;q) associated with the root system (C₁v,C₁). We display three elements x, y, z in H that satisfy essentially the Z₃-symmetric Askey-Wilson relations. We obtain the relations as follows. We work with an algebra Ĥ that is more general than H, called the universal double affine Hecke algebra of type (C₁v,C₁). An advantage of Ĥ over H is that it is parameter free and has a larger automorphism group. We give a surjective algebra homomorphism Ĥ → H. We define some elements x, y, z in Ĥ that get mapped to their counterparts in H by this homomorphism. We give an action of Artin's braid group B₃ on Ĥ that acts nicely on the elements x, y, z; one generator sends x → y → z → x and another generator interchanges x, y. Using the B₃ action we show that the elements x, y, z in Ĥ satisfy three equations that resemble the Z₃-symmetric Askey-Wilson relations. Applying the homomorphism Ĥ → H we find that the elements x, y, z in H satisfy similar relations.
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| Date |
2019-02-09T20:27:33Z
2019-02-09T20:27:33Z 2010 |
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| Type |
Article
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| Identifier |
Double Affine Hecke Algebras of Rank 1 and the Z₃-Symmetric Askey-Wilson Relations / T. Ito, P. Terwilliger // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 17 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 33D80; 33D45 DOI:10.3842/SIGMA.2010.065 http://dspace.nbuv.gov.ua/handle/123456789/146531 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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