The classical wreath product G ≀ Σd is a semidirect product Gd ⋊ Σd with Σd acting on Gd by permutations. We deform this classical wreath product by deforming G into an associative algebra B, deforming Σd into a Hecke algebra, and deforming the action. The result is called a quantum wreath product B ≀ 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.
This video was produced by the Okinawa Institute of Science and Technology, as part of their OIST Representation Theory Seminar series.
