The odd nilHecke algebra and its diagrammatics
arXiv:1111.1320 · doi:10.1093/imrn/rns240
Abstract
We introduce an odd version of the nilHecke algebra and develop an odd analogue of the thick diagrammatic calculus for nilHecke algebras. We graphically describe idempotents which give a Morita equivalence between odd nilHecke algebras and the rings of odd symmetric functions in finitely many variables. Cyclotomic quotients of odd nilHecke algebras are Morita equivalent to rings which are odd analogues of the cohomology rings of Grassmannians. Like their even counterparts, odd nilHecke algebras categorify the positive half of quantum sl(2).
48 pages, eps and xypic diagrams
References in corpus (3)
Cited by in corpus (25)
- Affine highest weight categories and affine quasihereditary algebras
- Quantum Supergroups III. Twistors
- Supercategorification of quantum Kac-Moody algebras II
- Categorification of quantum Kac-Moody superalgebras
- Super Kac-Moody 2-categories
- The differential graded odd nilHecke algebra
- Oddification of the cohomology of type A Springer varieties
- Quantum supergroups II. Canonical basis
- Categorification at prime roots of unity and hopfological finiteness
- Quantum Supergroups I. Foundations
- DG structures on odd categorified quantum sl(2)
- Quantum osp(1|2n) knot invariants are the same as quantum so(2n+1) knot invariants
- Odd Grassmannian bimodules and derived equivalences for spin symmetric groups
- Odd Khovanov homology for tangles
- Frobenius nilHecke algebras
- On 2-Verma modules for quantum
- Higher Representation Theory and Quantum Affine Schur-Weyl Duality
- Clifford-symmetric polynomials
- Not even Khovanov homology
- A geometric setting for quantum osp(1|2)
- q-symmetric functions and q-quasisymmetric functions
- Quantum supergroups IV. The modified form
- Schubert Class and cyclotomic nilHecke algebras
- Odd Dunkl Operators and nilHecke Algebras
- The odd Littlewood-Richardson rule