Action of the Witt algebra on categorified quantum groups

2025/07/02 by Grlj, Jernej, Lauda, Aaron D.
#17B10 #18N25 #57K16 #57K18 #81R10 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.01877

Abstract

We construct an action of the positive Witt algebra on the categorified quantum group associated to a simply-laced Lie algebra. In the type A case, we show that this action induces an action of the positive Witt algebra on \mathfrakgl_n-foams, recovering the action of Qi, Robert, Sussan, and Wagner. We also show that this construction is compatible with the trace decategorification, inducing the action of the positive Witt algebra on the current algebra.

Citations

• An action of the Witt algebra on Khovanov-Rozansky homology
• The \mathfraksl_n foam 2-category: a combinatorial formulation of Khovanov-Rozansky homology via categorical skew Howe duality
• Positive half of the Witt algebra acts on triply graded link homology
• Quiver Hecke algebras and 2-Lie algebras
• A diagrammatic categorification of the q-Schur algebra
• 2-Kac-Moody algebras

Related

• Symmetries of \mathfrakgl_N-foams
• Quantum algebras and Lie groups
• Jones-Witten Invariants for Nonsimply-Connected Lie Groups and The Geometry of the Weyl Alcove
• Trace decategorification of tensor product algebras
• Categorification of the adjoint action of quantum groups