Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology

Details Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology Modified regular representations of affine and Virasoro algebras, VOA structure and semi-infinite cohomology

2004-09-07

arxiv.org/abs/math/0409117v1

Mathematics

Quantum Algebra

39 pages

Scientific paper

We identify the algebra of matrix elements of big projective modules in category O with the regular functions on the big Bruhat cell of G. Analogous extensions of the regular representations of the affine Lie and Virasoro algebras yield vertex operator algebras, equipped with two commuting actions with special values of the total central charge. In the generic case, we identify the structure of these VOAs, compute their semi-infinite cohomology. Its superalgebra structure encodes the fusion rules for the associated tensor categories. Full details are provided for the affine sl(2) and Virasoro algebras, and various generalizations and extensions are discussed.

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