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.