An approach to categorification of Verma modules

Abstract

We give a geometric categorification of the Verma modules $M(\lambda )$ for quantum ${\mathfrak{sl}}_2$.

v4: 60 pages, new subsection 5.3 on fields of formal Laurent series and cone bounded modules + minor corrections. v3: 58 pages, new section on completed Grothendieck groups. v2: 44 pages, Section 6 rewritten, improved exposition

References in corpus (8)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• Knot invariants and higher representation theory
• Derived equivalences for symmetric groups and sl\_2-categorification
• An odd categorification of quantum sl(2)
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• The b-functions for prehomogeneous vector spaces of commutative parabolic type and generalized universal Verma modules

Cited by in corpus (6)

• Tensor product categorifications, Verma modules and the blob 2-category
• DG-Enhanced Hecke and KLR Algebras
• Categorification of infinite-dimensional ${\mathfrak{sl}}_2$-modules and braid group 2-actions I: tensor products
• Spectral 2-actions, foams, and frames in the spectrification of Khovanov arc algebras
• Enhanced nilHecke algebras and baby Verma modules
• Asymptotic Grothendieck groups and c.b.l.f. positive dg-algebras