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Langlands Duality for Representations and Quantum Groups at a Root of Unity

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Abstract

We give a representation-theoretic interpretation of the Langlands character duality of [FH], and show that the “Langlands branching multiplicities” for symmetrizable Kac-Moody Lie algebras are equal to certain tensor product multiplicities. For finite type quantum groups, the connection with tensor products can be explained in terms of tilting modules.

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Authors and Affiliations

  1. Department of Mathematics, Imperial College London, London, SW7 2AZ, United Kingdom

    Kevin McGerty

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  1. Kevin McGerty
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Correspondence to Kevin McGerty.

Additional information

Communicated by Y. Kawahigashi

Supported by a Royal Society University Research Fellowship.

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McGerty, K. Langlands Duality for Representations and Quantum Groups at a Root of Unity. Commun. Math. Phys. 296, 89–109 (2010). https://doi.org/10.1007/s00220-010-0993-z

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  • DOI: https://doi.org/10.1007/s00220-010-0993-z

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