Categorical diagonalization of full twists

Abstract

We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of categorical diagonalization introduced earlier by the authors. We prove our conjecture in type $A$, and as a result we obtain a categorification of the Young idempotents.

References in corpus (2)

• A geometric construction of colored HOMFLYPT homology
• A categorification of the stable SU(2) Witten-Reshetikhin-Turaev invariant of links in S2 x S1

Cited by in corpus (7)

• Categorified Young symmetrizers and stable homology of torus links
• Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types
• Khovanov polynomials for satellites and asymptotic adjoint polynomials
• Khovanov homology for links in ${\#}^r(S^2\times S^1)$
• Localized calculus for the Hecke category
• Homology Groups and Categorical Diagonalization
• Constructing categorical idempotents