An abelian formula for the quantum Weyl group action of the coroot lattice Article Swipe
Siddharth Gautam
,
Valerio Toledano-Laredo
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2501.02365
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2501.02365
Let g be a complex simple Lie algebra and Uq(Lg) its quantum loop algebra, where q is not a root of unity. We give an explicit formula for the quantum Weyl group action of the coroot lattice Q of g on finite-dimensional representations of Uq(Lg) in terms of its commuting generators. The answer is expressed in terms of the Chari-Pressley series, whose evaluation on highest weight vectors gives rise to Drinfeld polynomials. It hinges on a strong rationality result for that series, which is derived in the present paper. As an application, we identify the action of Q on the equivariant K-theory of Nakajima quiver varieties with that of explicitly given determinant line bundles.
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- preprint
- Language
- en
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- http://arxiv.org/abs/2501.02365
- https://arxiv.org/pdf/2501.02365
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https://doi.org/10.48550/arxiv.2501.02365Digital Object Identifier
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An abelian formula for the quantum Weyl group action of the coroot latticeWork title
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preprintOpenAlex work type
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enPrimary language
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2025Year of publication
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2025-01-04Full publication date if available
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Siddharth Gautam, Valerio Toledano-LaredoList of authors in order
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https://arxiv.org/abs/2501.02365Publisher landing page
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https://arxiv.org/pdf/2501.02365Direct link to full text PDF
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://arxiv.org/pdf/2501.02365Direct OA link when available
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Abelian group, Lattice (music), Quantum, Action (physics), Mathematical physics, Group (periodic table), Theoretical physics, Physics, Quantum mechanics, Mathematics, Pure mathematics, AcousticsTop concepts (fields/topics) attached by OpenAlex
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