Weyl modules for classical and quantum affine algebras

By Vyjayanthi Chari, A. Pressley. 2000

282 citations recorded by the source corpus.

We define a family of universal finite-dimensional highest weight modules for affine Lie algebras, we call these Weyl modules. We conjecture that these are the classical limits of the irreducible finite--dimensional representations of the quantum affine algebras. We prove this conjecture in the case of affine sl_2. We establish a criterion for these modules to be irreducible and prove a factorization theorem for them in the general case.

Subfields: Algebra and Number Theory, Atomic and Molecular Physics, and Optics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/371147c49f13acd3476674a2f10ed763d0d9a072

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In Algebra and Number Theory

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Citations in the corpus

Braid group actions and tensor products (2001, methodology): “Part (ii) was proved in [CP4], (see also [VV], [N2] in the case when π(u) ∈ C[q, q, u].”
Demazure Modules, Fusion Products and Q-Systems (2013, background): “It was proved in [11] (see also [7]) that the local Weyl modules are finite–dimensional and so, in particular, we have (xα ⊗ 1) wλ = 0, α ∈ R .”
Weyl modules, Demazure modules, KR-modules, crystals, fusion products and limit constructions (2005, background): “It was conjectured in [10] (and proved in the sl2-case) that the dimension of the Weyl modules depend only λπq , respectively λπ .”
Affine highest weight categories and affine quasihereditary algebras (2014, background): “Here we follow [10], see also [11], [5], [6], [9] and references therein.”