OIST Representation Theory Seminar: Quantum wreath product

Title: Quantum wreath product

Ziqing Xiang, Southern University of Science and Technology

Abstract: The classical wreath product $G \wr \Sigma_d$ is a semidirect product $G^d \rtimes \Sigma_d$ with $\Sigma_d$ acting on $G^d$ by permutation. We deform this classical wreath product by deforming $G$ into an associative algebra $B$, deforming $\Sigma_d$ into a Hecke algebra, and deforming the action. The result is called a quantum wreath product $B \wr H(d)$. Many variants of Hecke algebras can be viewed as quantum wreath products, hence could be treated in a unified manner.

In this talk, we will discuss necessary and sufficient conditions for quantum wreath products to have a basis of suitable size. We will also discuss some other structural results, the Schur algebras of these quantum wreath products, and their representations.

Meeting ID: 97881067465, password will be announced 24 hours before the talk.