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
Date:2020
Main Author: Rembado, Gabriele
Format: Article
Language:English
Published: Інститут математики НАН України 2020
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
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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.
first_indexed 2026-04-17T15:52:50Z
format Article
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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