Annular webs and Levi subalgebras

Tubbenhauer, Daniel;Dos Santos Santana Forte Vaz, Pedro;Lacabanne, Abel
(2023) journal of combinatorial algebra — Vol. 3/4, p. 283-326 (2023)

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Abstract
For any Levi subalgebra of the form 𝔩=𝔤𝔩l1⊕⋯⊕𝔤𝔩ld⊆𝔤𝔩n we construct a quotient of the category of annular quantum 𝔤𝔩n webs that is equivalent to the category of finite dimensional representations of quantum 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 𝔩 by additive idempotent completion, and a web version of the generalized blob algebra.
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Tubbenhauer, D., Dos Santos Santana Forte Vaz, P., & Lacabanne, A. (2023). Annular webs and Levi subalgebras. journal of combinatorial algebra, 3/4, 283-326. https://doi.org/10.4171/JCA/76 (Original work published 2023)