Annular webs and Levi subalgebras

Abstract

For any Levi subalgebra of the form $\mathfrak{l}={\mathfrak{gl}}_{l_1}\oplus \cdots \oplus {\mathfrak{gl}}_{l_d}\subseteq {\mathfrak{gl}}_n$ we construct a quotient of the category of annular quantum ${\mathfrak{gl}}_n$ webs that is equivalent to the category of finite-dimensional representations of quantum $\mathfrak{l}$ generated by exterior powers of the vector representation. This can be interpreted as an annular version of skew Howe duality, gives a description of the representation category of $\mathfrak{l}$ by additive idempotent completion, and a web version of the generalized blob algebra.