The Universal Askey-Wilson Algebra
نویسندگان
چکیده
منابع مشابه
The Universal Askey–Wilson Algebra
Let F denote a field, and fix a nonzero q ∈ F such that q 6= 1. We define an associative F-algebra ∆ = ∆q by generators and relations in the following way. The generators are A, B, C. The relations assert that each of A+ qBC − q−1CB q2 − q−2 , B + qCA− q−1AC q2 − q−2 , C + qAB − q−1BA q2 − q−2 is central in ∆. We call ∆ the universal Askey–Wilson algebra. We discuss how ∆ is related to the orig...
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The Askey–Wilson algebras were used to interpret the algebraic structure hidden in the Racah–Wigner coefficients of the quantum algebra Uq(sl2). In this paper, we display an injection of a universal analog △q of Askey–Wilson algebras into Uq(sl2) ⊗ Uq(sl2) ⊗ Uq(sl2) behind the application. Moreover we formulate the decomposition rules for 3-fold tensor products of irreducible Verma Uq(sl2)-modu...
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Let F denote a field, and fix a nonzero q ∈ F such that q 6= 1. The universal Askey–Wilson algebra is the associative F-algebra ∆ = ∆q defined by generators and relations in the following way. The generators are A, B, C. The relations assert that each of A+ qBC − q−1CB q2 − q−2 , B + qCA− q−1AC q2 − q−2 , C + qAB − q−1BA q2 − q−2 is central in ∆. In this paper we discuss a connection between ∆ ...
متن کاملThe Universal Askey – Wilson Algebra and DAHA of Type ( C ∨ 1 , C 1 )
Let F denote a field, and fix a nonzero q ∈ F such that q 6= 1. The universal Askey–Wilson algebra ∆q is the associative F-algebra defined by generators and relations in the following way. The generators are A, B, C. The relations assert that each of A+ qBC − q−1CB q2 − q−2 , B + qCA− q−1AC q2 − q−2 , C + qAB − q−1BA q2 − q−2 is central in ∆q. The universal DAHA Ĥq of type (C ∨ 1 , C1) is the a...
متن کاملThe Associated Askey-wilson Polynomials
We derive some contiguous relations for very well-poised 8<^7 series and use them to construct two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials. We then use these solutions to find explicit representations of two families of associated Askey-Wilson polynomials. We identify the corresponding continued fractions as quotients of tw...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2011
ISSN: 1815-0659
DOI: 10.3842/sigma.2011.069