Journal
NUCLEAR PHYSICS B
Volume 698, Issue 3, Pages 409-449Publisher
ELSEVIER
DOI: 10.1016/j.nuclphysb.2004.06.056
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We construct W-algebra generalizations of the sl(2) algebra-W algebras W-n((2)) generated by two currents epsilon and F with the highest pole of order n in their OPE. The n = 3 term in this series is (2) the Bershadsky-Polyakov W-3((2)) algebra. We define these algebras as a centralizer (commutant) of the U(q)sl(n\l) quantum supergroup and explicitly find the generators in a factored, Miura-like (2) form. Another construction of the W-n((2)) algebras is in terms of the coset sl(n\1)/sl(n). The relation between the two constructions involves the duality (k + n - 1)(k' + n - 1) = 1 between levels k and k' of two sl(n) algebras. (C) 2004 Published by Elsevier B.V.
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