Superalgebra deformations of web categories

Abstract: For a superalgebra A, and even subalgebra a, one may define an associated diagrammatic monoidal supercategory Web(A,a), which generalizes a number of symmetric web category constructions. In this talk, I will define and discuss Web(A,a), focusing on two interesting applications: Firstly, Web(A,a) is equipped with an asymptotically faithful functor to the category of gl_n(A)-modules generated by symmetric powers of the natural module, and may be used to establish Howe dualities between gl_n(A) and gl_m(A) in some cases. Secondly, Web(A,a) yields a diagrammatic presentation for the ‘Schurification' T^A_a(n,d). For various choices of A/a, these Schurifications have proven connections to RoCK blocks of Hecke algebras, and conjectural connections to RoCK blocks of Schur algebras and Sergeev superalgebras. This is joint work with Nicholas Davidson, Jonathan Kujawa, and Jieru Zhu.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.