Lie algebras and recurrence relations III:q-analogs and quantized algebras |
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Authors: | Philip Feinsilver |
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Institution: | (1) Department of Mathematics, Southern Illinois University, 62901 Carbondale, IL, USA |
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Abstract: | q-Analogs of the basic structures discussed in Lie Algebras and Recurrence Relations I are presented. Theq-Heisenberg-Weyl (qHW) and qsl(2) algebras are discussed in detail. Presently it is known that such structures are very closely tied in with the theory of quantum groups. Among other topics, coherent state representations and their interpretations asq-identities forq-Hermite and Al-Salam-Chihara (q-Meixner) polynomials are discussed. A discussion of Clebsch-Gordan coefficients for a qsu(2)-type algebra is presented. |
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Keywords: | Primary 16A68 17B99 22E99 secondary 33A99 47B39 81C40 |
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