Title: Polynomial quantum wreath products

Speaker: Chun-Ju Lai (Academia Sinica)

Abstract: Recently, there have been several work defining various analogs of affine Hecke and Schur algebras, e.g. Kleshchev-Muth (motivated by Turner's conjectures about blocks of symmetric groups), Miemietz-Stroppel (motivated by representations of p-adic GL_n), and Song-Wang (who consider diagrammatic presentations from a monoidal category perspective). I will introduce a serious attempt to unify and generalize these many variations, called the quantum wreath products, which afford nice structure and representation theory such as the existence of PBW bases, and Schur-Weyl duality. We will focus on the quantum wreath products of polynomial type and use Vigneras' pro-p Iwahori-Hecke algebras for GL_n as a running example. 

Funding: Basic Science Grant.