Coulomb branches and affine quantum groups / Branches de Coulomb et groupes quantiques affines

Collection Coulomb branches and affine quantum groups / Branches de Coulomb et groupes quantiques affines

Organizer(s) Hernandez, David ; Shan, Peng ; Varagnolo, Michela ; Vasserot, Eric

Date(s) 06/07/2026 - 10/07/2026

linked URL https://conferences.cirm-math.fr/3599.html

00:00:00 / 00:00:00

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On the Hernandez conjecture

In 2004, Nakajima established a unified Kazhdan-Lusztig type algorithm to compute the q-characters of finite-dimensional simple representations of quantum affine algebras of simply-laced types in a geometric manner. Hernandez showed that a similar algorithm can be formulated for non-simply laced types as well, and conjectured that it actually computes the simple q-characters. In this talk, I will report recent progress toward this conjecture, including its proof in classical types, based on joint works with Hernandez, Oh, Oya, and with Qin.

Information about the video

Date of recording 06/07/2026
Date of publication 03/08/2026
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Luca Recanzone
Format MP4

Citation data

DOI 10.24350/CIRM.V.20513103
Cite this video Fujita, Ryo (06/07/2026). On the Hernandez conjecture. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20513103
URL https://dx.doi.org/10.24350/CIRM.V.20513103

Domain(s)

Bibliography

FUJITA, Ryo, HERNANDEZ, David, OH, Se-jin, et al. Isomorphisms among quantum Grothendieck rings and propagation of positivity. Journal für die reine und angewandte Mathematik (Crelles Journal), 2022, vol. 2022, no 785, p. 117-185. - https://doi.org/10.1515/crelle-2021-0088
FUJITA, Ryo et QIN, Fan. Freezing operators in representation theory of quantum loop algebras. arXiv preprint arXiv:2601.00687, 2026. - https://doi.org/10.48550/arXiv.2601.00687

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