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Unitary Representations of Su_q(2) on the Plane for q in R+ or Generic q in S1 | | M. Irac-Astaud
; C. Quesne
; | | Date: |
9 Jul 1998 | | Subject: | Quantum Algebra | math.QA | | Affiliation: | Laboratoire de Physique Théorique de la Matière Condensée, Université Paris VII, Paris, France), C. Quesne (Physique Nucléaire Théorique et Physique Mathématique, Université Libre de Bruxelles, Ca | | Abstract: | Some time ago, Rideau and Winternitz introduced a realization of the quantum algebra su_q(2) on a real two-dimensional sphere, or a real plane, and constructed a basis for its representations in terms of q-special functions, which can be expressed in terms of q-Vilenkin functions. In their study, the values of q were implicitly restricted to q in R^+. In the present paper, we extend their work to the case of generic values of q in S^1 (i.e., q values different from a root of unity). In addition, we unitarize the representations for both types of q values, q in R^+ and generic q in S^1, by determining some appropriate scalar products. | | Source: | arXiv, math.QA/9807046 | | Services: | Forum | Review | PDF | Favorites | |
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