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Irrational free field resolutions forW(sl(n)) and extended Sugawara construction

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Abstract

The existence of Miura-type free field realizations is established for the extended conformal algebrasW(sl(n)) at irrational values of the screening parameter. The problem of the “closure” of the algebra is reduced to a finite dimensional quantum group problem. The structure of the Fock space resolution and the character formula are obtained for the irreducible modules. As graded vector spaces these modules are shown to be isomorphic to the space ofsl(n) singlets in\(\widehat{sl}(n)\) affine level 1 modules. The isomorphism is given by the ϕβγ free field realization of\(\widehat{sl}(n)\).

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  1. II. Institute for Theoretical Physics, University of Hamburg, Luruper Chaussee 149, W-2000, Hamburg 50, Germany

    M. Niedermaier

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Communicated by N.Yu. Reshetikhin

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Niedermaier, M. Irrational free field resolutions forW(sl(n)) and extended Sugawara construction. Commun.Math. Phys. 148, 249–281 (1992). https://doi.org/10.1007/BF02100861

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