The Odd nilHecke Algebra and its Diagrammatics

By Alexander P. Ellis, Mikhail Khovanov, Aaron D. Lauda. 2011

54 citations recorded by the source corpus.

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).

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5efab25ee8d2d37e9bece80a2ed8ad8e27aba08b

How researchers see this paper

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In Algebra and Number Theory

1. Alexander S. Kleshchev
2. Jonathan Brundan
3. Arun Ram
4. Aaron D. Lauda
5. Mikhail Khovanov
6. Raphaël Rouquier
7. Weiqiang Wang
8. A. Premet

In Discrete Mathematics and Combinatorics

1. Alexander S. Kleshchev
2. Jonathan Brundan
3. Aaron D. Lauda
4. Arun Ram
5. Mikhail Khovanov
6. Raphaël Rouquier

In Geometry and Topology

1. Alexander S. Kleshchev
2. Jonathan Brundan
3. Arun Ram
4. Ben Webster
5. Aaron D. Lauda
6. I. Losev
7. Raphaël Rouquier
8. C. Stroppel

Citations in the corpus

• Affine highest weight categories and affine quasihereditary algebras (2014, background): “an be found in [47]. The categories of Khovanov and Sazdanovich [29] used to category Hermite polynomials seem to be B-highest weight for B the class of nilCoxeter algebras. The odd nilHecke algebras [19] and quiver Hecke(-Clifford) superalgebras of [22] should satisfy the (super analogue of) the axi”