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.