Lie algebra cohomology and the fusion rules

DOI10.1007/BF02101235zbMath0842.17038WikidataQ115392796 ScholiaQ115392796MaRDI QIDQ1901811

Constantin Teleman

Publication date: 6 August 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Lie algebra cohomologyfusion rulesvanishing theoremBorel-Weil-Bott theoremholomorphic induction maploop group analogue

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) Loop groups and related constructions, group-theoretic treatment (22E67) Cohomology of Lie (super)algebras (17B56)

Related Items (15)

Braided tensor categories of admissible modules for affine Lie algebras ⋮ PRV for the fusion product, the case \(\lambda \gg \mu \) ⋮ A Weyl module stratification of integrable representations. With an appendix by Ryosuke Kodera ⋮ Dirac induction for loop groups ⋮ Twisted conformal blocks and their dimension ⋮ Twisted strong Macdonald theorems and adjoint orbits ⋮ A Brylinski filtration for affine Kac-Moody algebras ⋮ Twenty five years of two-dimensional rational conformal field theory ⋮ Explicit determination of the Picard group of moduli spaces of semistable \(G\)-bundles on curves ⋮ Unitarity of the modular tensor categories associated to unitary vertex operator algebras. II. ⋮ Twisted representation rings and Dirac induction ⋮ Conformal embedding and twisted theta functions at level one ⋮ Non-negative integral level affine Lie algebra tensor categories and their associativity isomorphisms ⋮ Generalized theta functions, strange duality, and odd orthogonal bundles on curves ⋮ Conformal blocks, Verlinde formula and diagram automorphisms

Cites Work

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• Cohomology of some nilpotent subalgebras of the Virasoro and Kac-Moody Lie algebras
• Homogeneous vector bundles
• Fusion rules and modular transformations in 2D conformal field theory
• The geometry of loop groups
• Demazure character formula in arbitrary Kac-Moody setting
• Lie algebra cohomology and the generalized Borel-Weil theorem
• The semi-infinite homology of Kac-Moody and Virasoro Lie algebras
• Semi-infinite cohomology and string theory

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