Seminar in Representation Theory
Quantum wreath products and highest weight covers
2025/08/07 (Thu.) 13:00~15:00
- Date : 2025/08/07 (Thu.) 13:00~15:00
- Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
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Speaker : Chun-Ju Lai (Institute of Mathematics, Academia Sinica)
- Abstract : In the first half, I'll describe a uniform construction of modules over the quantum wreath products, using parabolic inductions on tensor products of the "wreath modules" introduced by Lai, Nakano and Xiang. This allows us to parametrize the sets of simples over the Ariki-Koike algebra, summands of the Kashiwara-Miwa-Stern module over the affine Hecke algebra, and Specht modules over the Hu algebra. In the second half, I'll talk about a general theory that determines whether a Schur functor for finite dimensional algebras is a 1-faithful quasi-hereditary cover. As an application, we show that the Schur functor for the Hu algebra is a 1-cover using a spectral sequence for the Specht modules constructed in the first half, and in turn solve the Ginzburg-Guay-Opdam-Rouquier problem of type D.
