Langlands duality for representations and quantum groups at a root of unity

Details Langlands duality for representations and quantum groups at a root of unity Langlands duality for representations and quantum groups at a root of unity

2009-02-09

arxiv.org/abs/0902.1485v3

Mathematics

Quantum Algebra

Final version

Scientific paper

We give a representation-theoretic interpretation of the Langlands character
duality of Frenkel and Hernandez, 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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