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
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Dedicated to our friend Daniel Arnaudon
Submitted: January 13, 2006; Accepted: March 6, 2006
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Arnaudon, D., Avan, J., Frappat, L. et al. Sugawara and Vertex Operator Constructions for Deformed Virasoro Algebras. Ann. Henri Poincaré 7, 1327–1349 (2006). https://doi.org/10.1007/s00023-006-0282-8
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DOI: https://doi.org/10.1007/s00023-006-0282-8