Global Weyl modules for thin Lie algebras are finite-dimensional

Dotsenko, Vladimir; Mozgovoy, Sergey

doi:10.5802/art.37

Dotsenko, Vladimir ; Mozgovoy, Sergey

Annals of Representation Theory, Volume 3 (2026) no. 1, pp. 141-163

Abstract

The notion of Weyl modules, both local and global, goes back to Chari and Pressley in the case of affine Lie algebras, and has been extensively studied for various Lie algebras graded by root systems. We extend that definition to a certain class of Lie algebras graded by weight lattices and prove that if such a Lie algebra satisfies a natural “thinness” condition, then already the global Weyl modules are finite-dimensional. Our motivating example of a thin Lie algebra is the Lie algebra of polynomial Hamiltonian vector fields on the plane vanishing at the origin. We also introduce stratifications of categories of modules over such Lie algebras and identify the corresponding strata categories.

Article information
Cite this article

Received: 2025-03-04
Revised: 2025-12-20
Accepted: 2026-03-24
Published online: 2026-05-11

DOI: 10.5802/art.37

Classification: 17B10, 16D90, 18G05, 18G25
Keywords: Hamiltonian Lie algebra, stratified category, Weyl module

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CC-BY 4.0

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Dotsenko, Vladimir; Mozgovoy, Sergey. Global Weyl modules for thin Lie algebras are finite-dimensional. Annals of Representation Theory, Volume 3 (2026) no. 1, pp. 141-163. doi: 10.5802/art.37

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