An abelian formula for the quantum Weyl group action of the coroot lattice
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866913157390270464 |
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| author | Gautam, S. Toledano-Laredo, V. |
| author_facet | Gautam, S. Toledano-Laredo, V. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_02365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An abelian formula for the quantum Weyl group action of the coroot lattice Gautam, S. Toledano-Laredo, V. Quantum Algebra Algebraic Geometry Representation Theory 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. |
| title | An abelian formula for the quantum Weyl group action of the coroot lattice |
| topic | Quantum Algebra Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2501.02365 |