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Sugawara and Vertex Operator Constructions for Deformed Virasoro Algebras

Authors:	Daniel Arnaudon Jean Avan Luc Frappat Eric Ragoucy Junichi Shiraishi

Institution:	(1) Laboratoire d’Annecy-le-Vieux de Physique Théorique, LAPTH, UMR 5108, CNRS and Université de Savoie, B.P. 110, F-74941 Annecy-le-Vieux Cedex, France;(2) Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, 5 mail Gay-Lussac Neuville-sur-Oise, F-95031 Cergy-Pontoise Cedex, France;(3) Graduate School of Mathematical Science, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8914, Japan

Abstract:	From the defining exchange relations of the $\mathcal{A}_{{q,p}} {\left( {\widehat{{gl}}_{N} } \right)}$ elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions relating the parameters p, q, N and the central charge c are shown to be related to the singularity structure of the functional coefficients defining the exchange relations of specific vertex operators representations of $\mathcal{A}_{{q,p}} {\left( {\widehat{{gl}}_{N} } \right)}$ available when N = 2. Communicated by Petr Kulish Submitted: January 13, 2006; Accepted: March 6, 2006 Dedicated to our friend Daniel Arnaudon

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