Date/Time : 14 May 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Feiyue Huang, Beijing Normal University

In the study of blocks of Ariki–Koike algebras, the Uglov map—the essential link connecting multipartitions to partitions—originates from Frenkel’s level-rank duality of type $A^{(1)}$ affine Lie algebras on Fock space. Inspired by this result, we develop an analogous framework for each classical affine type once the corresponding level-rank duality is established. In this talk, we construct appropriate Fock spaces for all classical affine Lie algebras and introduce the associated combinatorial models, specifically Maya diagrams and abaci. By analyzing the action of the Virasoro algebra, we completely characterize the joint highest weight vectors in the Fock space, thereby formulating the corresponding level-rank duality theory. Using this new theory, we generalize the results of Fayers, Jacon-Lecouvey and Li-Qi et al. on block invariants of Ariki–Koike algebras, and provide combinatorial models for block invariants of cyclotomic KLR algebras for each classical affine type. This talk is based on a joint work with Wei Hu, Yanbo Li and Xiangyu Qi.

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Date/Time : 12 May 2026 14:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : LIU Jie, Chinese Academy of Sciences

I will report a joint work with Baohua Fu proving that most Hamiltonian reductions of cotangent bundles are affine closures of cotangent bundles, together with some applications.

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