Categorification of quantum Kac-Moody superalgebras

DOI10.1090/S0002-9947-2014-06128-XzbMath1355.17011arXiv1202.2769OpenAlexW2963796948MaRDI QIDQ5496627

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Publication date: 2 February 2015

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.2769

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Hecke algebras and their representations (20C08)

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Categorification of tensor powers of the vector representation of \(U_q(\mathfrak{gl}(1| 1))\) ⋮ Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras ⋮ Quantum supergroups. V: Braid group action ⋮ The differential graded odd nilHecke algebra ⋮ Irreducible Wakimoto-like modules for the Lie superalgebra \(D(2, 1;\alpha)\) ⋮ Quantum supergroups II. Canonical basis ⋮ R-matrix realization of two-parameter quantum affine algebra \(U_{r, s} (\hat{\mathfrak{gl}}_n)\) ⋮ Odd knot invariants from quantum covering groups ⋮ Supercategorification of quantum Kac-Moody algebras. I, II ⋮ A geometric setting for quantum 𝔬𝔰𝔭(1|2) ⋮ Graded dimensions and monomial bases for the cyclotomic quiver Hecke superalgebras ⋮ Canonical basis for quantum \(\mathfrak{osp}(1|2)\) ⋮ DG structures on odd categorified quantum \(sl(2)\) ⋮ Spin nilHecke algebras of classical type ⋮ Quantum supergroups. I: Foundations ⋮ Quantum supergroups. III: Twistors ⋮ Quantum supergroups. IV: The modified form ⋮ Young walls and graded dimension formulas for finite quiver Hecke algebras of type \(A^{(2)}_{2\ell}\) and \(D^{(2)}_{\ell+1}\) ⋮ Representations of quantum affine superalgebras ⋮ Graded Cartan determinants of the symmetric groups ⋮ Quantum supergroups. VI: Roots of 1 ⋮ A categorification of the positive half of quantum 𝑔𝑙(𝑚|1) ⋮ An odd categorification of \(U_q(\mathfrak{sl}_2)\)

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