Videos

Categorified i-quantum groups and spin link homology

Presenter
October 23, 2025
Abstract
i-Quantum group theory gives rise to q-deformed special orthogonal algebras different than Drinfeld-Jimbo quantum groups. These i-quantum special orthogonal algebras have mysterious nonclassical representations which do not q-deform finite dimensional representations of the special orthogonal algebra. The nonclassical representations do not immediately fit into the framework of Bao-Wang’s i-canonical basis or Brundan-Wang-Webster’s categorified i-quantum groups. One key to understanding nonclassical representations is Wenzl’s recent observation that they are afforded by quantum spin Howe duality in type B. In this talk, I will discuss evidence, coming from joint work with Elias-Rose on type B webs and type B link homology, that categorified quantum spin Howe duality in type B is just ``folded” categorified skew Howe duality in type A.