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We describe a relation between homological representations of the braid groups at roots of unity and the monodromy representations of the space of conformal blocks by using hypergeometric integrals. We give an isomorphism between the space of conformal blocks and the set of morphisms of the Temperley–Lieb–Jones category, which is equivariant under the action of the braid groups.

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Homological Representations of Braid Groups at Roots of Unity and the Space of Conformal Blocks

  • 会议论文

  • 发表日期：

    2025年

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  • Toshitake Kohno

摘要

We describe a relation between homological representations of the braid groups at roots of unity and the monodromy representations of the space of conformal blocks by using hypergeometric integrals. We give an isomorphism between the space of conformal blocks and the set of morphisms of the Temperley–Lieb–Jones category, which is equivariant under the action of the braid groups.