We introduce a new notion called the quantum wreath product, which produces an algebra B ≀Q H(d) from a given associative algebra B, a positive integer d, and a choice Q = (R, S, ρ, σ) of parameters. Important examples include many variants of the Hecke algebras, such as the Ariki-Koike algebras, the affine Hecke algebras and their degenerate version, Wan-Wang’s wreath Hecke algebras, Rosso-Savage’s (affine) Frobenius Hecke algebras, Kleshchev-Muth’s affine zigzag algebras, and the Hu algebra that quantizes the wreath product Σm ≀ Σ2 between symmetric groups. We will discuss the bases of quantum wreath product algebras, and some of their representations.
This is joint work with Daniel Nakano and Chun-Ju Lai.
This video is part of the University of Georgia‘s Algebra seminar.
