$W^{(2)}_n$ algebras

Details $W^{(2)}_n$ algebras $W^{(2)}_n$ algebras

2004-01-14

arxiv.org/abs/math/0401164v1

Nucl.Phys. B698 (2004) 409-449

Mathematics

Quantum Algebra

LaTeX: amsart++, xy, sidecap. 40pp

Scientific paper

10.1016/j.nuclphysb.2004.06.056

We construct W-algebra generalizations of the ^sl(2) algebra -- W-algebras W^{(2)}_n generated by two currents E and F with the highest pole of order n in their OPE. The n=3 term in this series is the Bershadsky--Polyakov algebra. We define these algebras as a centralizer (commutant) of the $U_{q}sl(n|1)$ super quantum group and explicitly find the generators in a factored, ``Miura-like'' form. Another construction of W^{(2)}_n 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.

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