Speaker: Satoshi Nawata (Fudan University)
Abstract: This talk will explore the representation theory of the spherical Double Affine Hecke Algebra (DAHA) of C^\vee C_1, using brane quantization. We will show an evidence of derived equivalence between A-brane category of character variety and representation category of DAHA. By examining the geometry of the Hitchin moduli space, I will demonstrate a one-to-one correspondence between finite-dimensional representations of the spherical DAHA and Lagrangian A-branes with compact support. This geometric approach reveals the action of affine braid group of type D_4 on the cateogry as auto-equivalence. This talk is based on an ongoing work with Junkang Huang, Yutai Zhang and Shutong Zhuang.
Time: 4:00 pm, Wednesday, 4th December, 2024
Location: Room 1610 at SIMIS, Block A, No. 657 Songhu Road, Yangpu District, Shanghai
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