Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2020
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| _version_ | 1866913799710179328 |
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| author | Felder, Giovanni Rembado, Gabriele |
| author_facet | Felder, Giovanni Rembado, Gabriele |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_14793 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks Felder, Giovanni Rembado, Gabriele Quantum Algebra Mathematical Physics Rings and Algebras Representation Theory 81T40, 17B38, 17B10 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 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. |
| title | Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks |
| topic | Quantum Algebra Mathematical Physics Rings and Algebras Representation Theory 81T40, 17B38, 17B10 |
| url | https://arxiv.org/abs/2012.14793 |