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arXiv · 2012.14793

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

Giovanni Felder·Gabriele Rembado
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Abstract

We give a mathematical definition of spaces of irregular vacua/covacua in genus zero, for any simple Lie algebra, working at generic noncritical level. This uses coinvariants of affine-Lie-algebra modules whose parameters match up with those of moduli spaces of irregular-singular meromorphic connections: the 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 somonodromy times \`a la Klar\`es, 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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BibTeXRIS

Giovanni Felder, Gabriele Rembado. 2020-12-29. Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks. https://doi.org/10.1007/s00029-022-00821-y

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