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Annular webs and Levi subalgebras

Published 2 Apr 2022 in math.QA, math.GT, and math.RT | (2204.00947v2)

Abstract: For any Levi subalgebra of the form $\mathfrak{l}=\mathfrak{gl}{l{1}}\oplus\dots\oplus\mathfrak{gl}{l{d}}\subseteq\mathfrak{gl}{n}$ 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.

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