Categorification of quantum symmetric pairs I

Abstract

We categorify a coideal subalgebra of the quantum group of ${\mathfrak{sl}}_{2r+1}$ by introducing a $2$-category à la Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-morphisms categorify the canonical basis of this algebra. This allows us to define a categorical action of this coideal algebra on the categories of modules over cohomology rings of partial flag varieties and on the BGG category $\mathcal{O}$ of type B/C.

final version, to appear in Quantum Topology

References in corpus (1)

• Derived equivalences for symmetric groups and sl\_2-categorification

Cited by in corpus (11)

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• Quiver varieties and symmetric pairs
• Lectures on dualities ABC in representation theory
• $ı$Hall algebras of weighted projective lines and quantum symmetric pairs
• The disoriented skein and iquantum Brauer categories
• Positivity of $ı$-canonical bases
• $ı$quantum groups of split type via derived Hall algebras
• Bubbles in the affine Brauer and Kauffman categories