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Deformed W_N algebras from elliptic sl(N) algebras

By J. Avan, L. Frappat, M. Rossi and P. Sorba

Abstract

We extend to the sl(N) case the results that we previously obtained on the construction of W_{q,p} algebras from the elliptic algebra A_{q,p}(\hat{sl}(2)_c). The elliptic algebra A_{q,p}(\hat{sl}(N)_c) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures indexed by N(N-1)/2 integers, defining q-deformations of the W_N algebra, are constructed. The operators t(z) also close an exchange algebra when (-p^1/2)^{NM} = q^{-c-N} for M in Z. It becomes Abelian when in addition p=q^{Nh} where h is a non-zero integer. The Poisson structures obtained in these classical limits contain different q-deformed W_N algebras depending on the parity of h, characterizing the exchange structures at p \ne q^{Nh} as new W_{q,p}(sl(N)) algebras.Comment: LaTeX2e Document - packages subeqn,amsfonts,amssymb - 30 page

Topics: Mathematics - Quantum Algebra, High Energy Physics - Theory, Nonlinear Sciences - Exactly Solvable and Integrable Systems, 81R50, 17B68
Publisher: 'Springer Science and Business Media LLC'
Year: 1998
DOI identifier: 10.1007/s002200050517
OAI identifier: oai:arXiv.org:math/9801105

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