Standard modules of quantum affine algebras

By M. Varagnolo, E. Vasserot. 2000

95 citations recorded by the source corpus.

We give a proof of the cyclicity conjecture of Akasaka-Kashiwara, for simply laced types, via quiver varieties. We get also an algebraic characterization of the standard modules.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/93cc7bbd3534cf75ceaf7c048d9c562503f836b4

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Representations of Quantum Affinizations and Fusion Product (2003, background): “The finite dimensional representations of quantum affine algebras are the subject of intense research (see, among the others, [AK], [CP1], [CP3], [CP4], [EM], [FR], [FM], [N1], [N2], [ VV2 ] and references therein).”
Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions (2005, background): “1], see [39] for the simply laced case) for twisted tensor products of cyclic modules implies a lower bound for the dimension:”
Quiver varieties and tensor products (2001, background): “Let Lg = g[x, x−1] be the loop algebra of g and let Uq(Lg) be the quantum loop algebra (the quantum affine algebra without centeral extension and degree Supported by the Grant-in-aid for Scientific Research (No.11740011), the Ministry of Education, Japan.”
Cherednik algebras, W-algebras and the equivariant cohomology of the moduli space of instantons on A2 (2012, methodology): “It was observed in [44] that, under Nakajima’s realization of affine quantum groups in terms of equivariant K-theory of quiver varieties, the coproduct of the quantum groups could be constructed geometrically using some fixed subsets of the quiver varieties.”