Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties
We will exhibit a group of symmetries of the simply-laced quantum connections, generalising the quantum/Howe duality relating KZ and the Casimir connection. These symmetries arise as a quantisation of the classical symmetries of the simply-laced isomonodromy systems, which in turn generalise the Har...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2020 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2020
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211017 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties. Gabriele Rembado. SIGMA 16 (2020), 103, 44 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862733577141092352 |
|---|---|
| author | Rembado, Gabriele |
| author_facet | Rembado, Gabriele |
| citation_txt | Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties. Gabriele Rembado. SIGMA 16 (2020), 103, 44 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We will exhibit a group of symmetries of the simply-laced quantum connections, generalising the quantum/Howe duality relating KZ and the Casimir connection. These symmetries arise as a quantisation of the classical symmetries of the simply-laced isomonodromy systems, which in turn generalise the Harnad duality. The quantisation of the classical symmetries involves constructing the quantum Hamiltonian reduction of the representation variety of any simply-laced quiver, both in filtered and in deformation quantisation.
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| first_indexed | 2026-04-17T15:52:50Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211017 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T15:52:50Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rembado, Gabriele 2025-12-22T09:29:35Z 2020 Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties. Gabriele Rembado. SIGMA 16 (2020), 103, 44 pages 1815-0659 2020 Mathematics Subject Classification: 81R99 arXiv:1905.07713 https://nasplib.isofts.kiev.ua/handle/123456789/211017 https://doi.org/10.3842/SIGMA.2020.103 We will exhibit a group of symmetries of the simply-laced quantum connections, generalising the quantum/Howe duality relating KZ and the Casimir connection. These symmetries arise as a quantisation of the classical symmetries of the simply-laced isomonodromy systems, which in turn generalise the Harnad duality. The quantisation of the classical symmetries involves constructing the quantum Hamiltonian reduction of the representation variety of any simply-laced quiver, both in filtered and in deformation quantisation. I thank Giovanni Felder for truly helpful discussions, Pavel Etingof and Travis Schedler for truly helpful e-mail exchanges, and Philip Boalch for both. This research began while the author was a member of the Laboratoire de Mathematiques d'Orsay, and was supported by a temporary research and teaching assistant contract; it was concluded while the author was a member of the Department of Mathematics at the ETH of Zurich, and was supported by the National Centre of Competence in Research "SwissMAP-The Mathematics of Physics" of the Swiss National Science Foundation. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties Article published earlier |
| spellingShingle | Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties Rembado, Gabriele |
| title | Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties |
| title_full | Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties |
| title_fullStr | Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties |
| title_full_unstemmed | Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties |
| title_short | Symmetries of the Simply-Laced Quantum Connections and Quantisation of Quiver Varieties |
| title_sort | symmetries of the simply-laced quantum connections and quantisation of quiver varieties |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211017 |
| work_keys_str_mv | AT rembadogabriele symmetriesofthesimplylacedquantumconnectionsandquantisationofquivervarieties |