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Type C blocks of super category $$\mathcal{O}$$. (English) Zbl 1446.17029
Authors’ abstract: “We show that the blocks of category $$\mathcal O$$ for the Lie superalgebra $$\mathfrak q_n(\mathbb C)$$ associated to half-integral weights carry the structure of a tensor product categorification for the infinite rank Kac-Moody algebra of type $$C_\infty$$. This allows us to prove two conjectures formulated by Cheng, Kwon and Wang. We then focus on the full subcategory consisting of finite-dimensional representations, which we show is a highest weight category with blocks that are Morita equivalent to certain generalized Khovanov arc algebras.”
The Lie superalgebra $$\mathfrak q_n(\mathbb C)$$ is the subalgebra of the general linear Lie superalgebra $$\mathfrak{gl}_{n|n}(\mathbb C)$$, consisting of matrices of the form $$\begin{pmatrix} A & B \\ B & A \end{pmatrix}$$. The main ingredient is some involved combinatorics related to tensor product modules over the Lie algebras $$\mathfrak{sl}_{+\infty}$$ and $$\mathfrak{sp}_{2\infty}$$.

##### MSC:
 17B45 Lie algebras of linear algebraic groups 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 17B37 Quantum groups (quantized enveloping algebras) and related deformations 17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
##### Keywords:
linear Lie superalgebra; category O
Zbl 1406.17014
Full Text:
##### References:
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