Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks

We give a mathematical definition of irregular conformal blocks in the genus-zero WZNW model for any simple Lie algebra, using coinvariants of modules for affine Lie algebras whose parameters match up with those of moduli spaces of irregular meromorphic connections: the open de Rham spaces. The Sega...

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Bibliographic Details
Published inSelecta mathematica (Basel, Switzerland) Vol. 29; no. 1
Main Authors Felder, Giovanni, Rembado, Gabriele
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2023
Springer Nature B.V
Subjects
Algebra
Lie groups
Mathematics
Mathematics and Statistics
Modules
Affine Lie algebras
Conformal field theory
17B10
Integrable quantum systems
81T40
Isomonodromic deformations
17B38
Irregular meromorphic connections
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Summary:We give a mathematical definition of irregular conformal blocks in the genus-zero WZNW model for any simple Lie algebra, using coinvariants of modules for affine Lie algebras whose parameters match up with those of moduli spaces of irregular meromorphic connections: the open de Rham spaces. The Segal–Sugawara representation of the Virasoro algebra is used to show that the spaces of irregular conformal blocks assemble into a flat vector bundle over the space of isomonodromy times à la Klarès, and we provide a universal version of the resulting flat connection generalising the irregular KZ connection of Reshetikhin and the dynamical KZ connection of Felder–Markov–Tarasov–Varchenko.
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ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-022-00821-y