Quantum Groups and Cohomology Theory of Quiver and Flag Varieties / Groupes quantiques et théories cohomologiques des variétés de drapeaux et variétés carquois

Collection Quantum Groups and Cohomology Theory of Quiver and Flag Varieties / Groupes quantiques et théories cohomologiques des variétés de drapeaux et variétés carquois

Organizer(s) Leclerc, Bernard ; Mihalcea, Leonardo ; Perrin, Nicolas ; Varagnolo, Michela

Date(s) 14/12/2020 - 18/12/2020

linked URL https://conferences.cirm-math.fr/2221.html

00:00:00 / 00:00:00

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Shifted quantum affine algebras, monoidal categorication and Langlands duality

By David Hernandez

Also appears in collection : ECM 2024 Invited Speakers

In the framework of the study of K-theoretical Coulomb branches, Finkelberg-Tsymbaliuk introduced remarkable new algebras, the shifted quantum affine algebras an their truncations, in the spirit of the shifted Yangians of Brundan-Kleshev, Braverman-Finkelberg Nakajima, Kamnitzer-Webster-Weekes-Yacobi... We discuss the following points in representation theory of (truncated) shifted quantum affine algebras that we relate to representations of Borel quantum affine algebras by induction and restriction functors. We establish that the Grothendieck ring of the category of finite-dimensional representations has a natural cluster algebra structure. We propose a conjectural parametrization of simple modules of a non simply-laced truncation in terms of the Langlands dual quantum affine Lie algebra. We have several evidences, including a general result for simple finite-dimensional representations proved by using the Baxter polynomiality of quantum integrable models.

Information about the video

Date of recording 14/12/2020
Date of publication 11/01/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19693103
Cite this video HERNANDEZ, David (14/12/2020). Shifted quantum affine algebras, monoidal categorication and Langlands duality. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19693103
URL https://dx.doi.org/10.24350/CIRM.V.19693103

Domain(s)

Bibliography

HERNANDEZ, David. Representations of shifted quantum affine algebras. arXiv preprint arXiv:2010.06996, 2020. - https://arxiv.org/abs/2010.06996

MSC codes

Document(s)

https://www.cirm-math.fr/RepOrga/2221/Slides/Hernandez-slides.pdf

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