Towards the theory of Yangians
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913254080512000 |
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| author | Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita |
| author_facet | Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita |
| contents | We review the main ideas underlying the emerging theory of Yangians -- the new type of hidden symmetry in string-inspired models. Their classification by quivers is a far-going generalization of simple Lie algebras classification by Dynkin diagrams. However, this is still a kind of project, while a more constructive approach goes through toric Calabi-Yau spaces, related supersymmetric systems and the Duistermaat-Heckmann/equivariant integrals between the fixed points in the ADHM-like moduli spaces. These fixed points are classified by crystals (Young-type diagrams) and Yangian generators describe ``instanton'' transitions between them. Detailed examples will be presented elsewhere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00760 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards the theory of Yangians Galakhov, Dmitry Morozov, Alexei Tselousov, Nikita High Energy Physics - Theory Mathematical Physics Algebraic Geometry Quantum Algebra Representation Theory We review the main ideas underlying the emerging theory of Yangians -- the new type of hidden symmetry in string-inspired models. Their classification by quivers is a far-going generalization of simple Lie algebras classification by Dynkin diagrams. However, this is still a kind of project, while a more constructive approach goes through toric Calabi-Yau spaces, related supersymmetric systems and the Duistermaat-Heckmann/equivariant integrals between the fixed points in the ADHM-like moduli spaces. These fixed points are classified by crystals (Young-type diagrams) and Yangian generators describe ``instanton'' transitions between them. Detailed examples will be presented elsewhere. |
| title | Towards the theory of Yangians |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2311.00760 |