Categorification of quantum Kac-Moody superalgebras

Abstract

We introduce a non-degenerate bilinear form and use it to provide a new characterization of quantum Kac-Moody superalgebras with no isotropic odd simple roots. We show that the spin quiver Hecke algebras introduced by Kang-Kashiwara-Tsuchioka provide a categorification of half the quantum Kac-Moody superalgebras, using the recent work of Ellis-Khovanov-Lauda. A new idea here is that a super sign is categorified as spin (i.e., the parity-shift functor).

v2. Minor typos corrected and references updated. To appear in Trans. AMS, Article ID TRAN6128

References in corpus (5)

• 2-Kac-Moody algebras
• Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
• The odd nilHecke algebra and its diagrammatics
• Categorifications from planar diagrammatics
• Supercategorification of quantum Kac-Moody algebras II

Cited by in corpus (14)

• Representations of Quantum Affine Superalgebras
• Quantum Supergroups III. Twistors
• Supercategorification of quantum Kac-Moody algebras II
• Oddification of the cohomology of type A Springer varieties
• Quantum supergroups II. Canonical basis
• Quantum Shuffles and Quantum Supergroups of Basic Type
• Quantum Supergroups I. Foundations
• Two-parameter quantum algebras, canonical bases and categorifications
• A categorification of the positive half of quantum gl(m|1)
• An identification of Lusztig's modified forms of quantum algebras and their analogues
• Higher Representation Theory and Quantum Affine Schur-Weyl Duality
• Quantum supergroups IV. The modified form
• A geometric setting for quantum osp(1|2)
• Young walls and graded dimension formulas for finite quiver Hecke algebras of type $A_{2\ell }^{(2)}$ and $D_{\ell +1}^{(2)}$