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Affine Kac-Moody algebras and semi-infinite flag manifolds. (English) Zbl 0722.17019
With the technique of semi-infinite cohomology over (affine) Kac-Moody algebras the authors realize so-called Wakimoto modules as twisted Verma modules. Among other wonders this brings about a two-sided resolution of these twisted Verma modules leading to a semi-infinite analog of the Borel-Weil-Bott theorem. The exposition is highly illuminating and equally breezy (lots of details are to be published).

17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
14M15 Grassmannians, Schubert varieties, flag manifolds
17B56 Cohomology of Lie (super)algebras
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
Full Text: DOI
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