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On the quantum group and quantum algebra approach toq-special functions

โœ Scribed by Roberto Floreanini; Luc Vinet


Publisher
Springer
Year
1993
Tongue
English
Weight
505 KB
Volume
27
Category
Article
ISSN
0377-9017

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๐Ÿ“œ SIMILAR VOLUMES


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โœ R. Floreanini; L. Vinet ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 543 KB

A quantum-algebraic framework for many \(q\)-special functions is provided. The twodimensional Euclidean quantum algebra, \(s l_{4}(2)\) and the \(q\)-oscillator algebra are considered. Realizations of these algebras in terms of operators acting on vector spaces of functions in one complex variable

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We derive the equivalence of the complex quantum enveloping algebra and the algebra of complex quantum vector fields for the Lie algebra types A., B., C n, and D. by factorizing the vector fields uniquely into a triangular and a unitary part and identifying them with the corresponding elements of th

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A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald symmetric functions. This is proved by constructing screeni