Two-parameter Langlands Correspondence
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911229161766912 |
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| author | Aganagic, Mina Frenkel, Edward Okounkov, Andrei |
| author_facet | Aganagic, Mina Frenkel, Edward Okounkov, Andrei |
| contents | In our paper arXiv:1701.03146 we established, for every simply-laced Lie algebra g, a canonical isomorphism between the spaces of deformed conformal blocks of the deformed W-algebra and the quantum affine algebra corresponding to g, which we view as a q-deformation of the quantum Langlands correspondence. This was done by realizing the deformed conformal blocks of these algebras via the quantum K-theory of the Nakajima quiver varieties. We also linked this isomorphism to a duality emerging from the 6d little string theory. Here, we give a brief survey of these results and propose an extension to the non-simply laced case, which exhibits a Langlands-type duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Two-parameter Langlands Correspondence Aganagic, Mina Frenkel, Edward Okounkov, Andrei Quantum Algebra High Energy Physics - Theory Mathematical Physics Algebraic Geometry Representation Theory In our paper arXiv:1701.03146 we established, for every simply-laced Lie algebra g, a canonical isomorphism between the spaces of deformed conformal blocks of the deformed W-algebra and the quantum affine algebra corresponding to g, which we view as a q-deformation of the quantum Langlands correspondence. This was done by realizing the deformed conformal blocks of these algebras via the quantum K-theory of the Nakajima quiver varieties. We also linked this isomorphism to a duality emerging from the 6d little string theory. Here, we give a brief survey of these results and propose an extension to the non-simply laced case, which exhibits a Langlands-type duality. |
| title | Two-parameter Langlands Correspondence |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2510.20948 |