Supercategorification of quantum Kac-Moody algebras II

Abstract

In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family of quantum superalgebras and their integrable highest weight modules. We show that, by taking a specialization, we obtain a supercategorification of quantum Kac-Moody superalgebras and their integrable highest weight modules.

The 1st version, 73 pages. The 2nd version, 75 pages with minor changes

References in corpus (5)

• 2-Kac-Moody algebras
• The odd nilHecke algebra and its diagrammatics
• Categorification of quantum Kac-Moody superalgebras
• Quantum Supergroups I. Foundations
• Biadjointness in cyclic Khovanov-Lauda-Rouquier Algebras

Cited by in corpus (12)

• Representations of Quantum Affine Superalgebras
• Quantum Supergroups III. Twistors
• Categorification of quantum Kac-Moody superalgebras
• Quantum supergroups II. Canonical basis
• Quantum Shuffles and Quantum Supergroups of Basic Type
• DG structures on odd categorified quantum sl(2)
• A cellular approach to the Hecke-Clifford superalgebra
• An identification of Lusztig's modified forms of quantum algebras and their analogues
• The center of a quantized enveloping algebra at an even root of unity
• Higher Representation Theory and Quantum Affine Schur-Weyl Duality
• A geometric setting for quantum osp(1|2)
• Quantum supergroups IV. The modified form