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Quantum character varieties at roots of unity
Multi angle
Authors : Safronov, Pavel (Author of the conference)
CIRM (Publisher )
14F05 - Sheaves, derived categories of sheaves and related constructions
14L24 - Geometric invariant theory of group schemes
17B63 - Poisson algebras
16T20 - Ring-theoretic aspects of quantum groups
CIRM (Publisher )
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Abstract :
Character varieties of closed surfaces have a natural Poisson structure whose quantization may be constructed in terms of the corresponding quantum group. When the quantum parameter is a root of unity, this quantization carries a central subalgebra isomorphic to the algebra of functions on the classical character variety. In this talk I will describe a procedure which allows one to obtain Azumaya algebras via quantum Hamiltonian reduction. As an application, I will show that quantizations of character varieties at roots of unity are Azumaya over the corresponding classical character varieties.
This is a report on joint work with Iordan Ganev and David Jordan.
MSC Codes : This is a report on joint work with Iordan Ganev and David Jordan.
14F05 - Sheaves, derived categories of sheaves and related constructions
14L24 - Geometric invariant theory of group schemes
17B63 - Poisson algebras
16T20 - Ring-theoretic aspects of quantum groups
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 18/04/2019 Conference Date : 02/04/2019 Subseries : Research talks arXiv category : Quantum Algebra ; Representation Theory Mathematical Area(s) : Algebra ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 01:02:09 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2019-04-02_Safronov.mp4 
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Information on the Event
Event Title : Symplectic representation theory / Théorie symplectique des représentationsEvent Organizers : Bellamy, Gwyn ; Ben-Zvi, David ; Schedler, Travis ; Schiffmann, Olivier ; Shan, Peng Dates : 01/04/2019 - 05/04/2019 Event Year : 2019 Event URL : https://conferences.cirm-math.fr/1956.html
Citation Data
DOI : 10.24350/CIRM.V.19511603Cite this video as: Safronov, Pavel (2019). Quantum character varieties at roots of unity. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19511603 URI : http://dx.doi.org/10.24350/CIRM.V.19511603 |
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Bibliography
- Ganev, I., Jordan, D., & Safronov, P. (2019). The quantum Frobenius for character varieties and multiplicative quiver varieties. arXiv:1901.11450 - https://arxiv.org/abs/1901.11450
