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The q-characters of representations of quantum affine algebras and deformations of W-algebras

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arxiv math/9810055 v5 pith:APLZ6NWM submitted 1998-10-08 math.QA hep-thnlin.SIsolv-int

Edward Frenkel , Nicolai Reshetikhin This is my paper · ORCID
classification math.QAhep-thnlin.SIsolv-int
keywords q-charactersaffinequantumrepresentationsalgebrashomomorphismringw-algebras
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We propose the notion of q-characters for finite-dimensional representations of quantum affine algebras. It is motivated by our theory of deformed W-algebras. We show that the q-characters give rise to a homomorphism from the Grothendieck ring of representations of a quantum affine algebra to a polynomial ring. We conjecture that the image of this homomorphism is equal to the intersection of certain "screening operators". We also discuss the connection between q-characters and Bethe Ansatz.

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Cited by 2 Pith papers

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  1. Gauge Origami and BPS/CFT correspondence

    hep-th 2025-02 conditional novelty 5.0 of 10

    The gauge origami partition function on C4 is realized as a correlation function of BPS qq-character operators, with D6 and D8 characters labeled by plane and solid partitions.

  2. Symmetries of Grothendieck rings in representation theory

    math.RT 2025-01 unverdicted

    A lecture-notes survey of cluster and Weyl group symmetries of Grothendieck rings, illustrated with quantum affine algebra examples.

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