Double Affine Hecke Algebras of Rank 1 and the Z₃-Symmetric Askey-Wilson Relations

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2010
• Hauptverfasser: Ito, T., Terwilliger, P.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2010
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/146531
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.

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...