The odd nilHecke algebra and its diagrammatics
Quantum Algebra
2014-03-18 v1 Representation Theory
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).
Keywords
Cite
@article{arxiv.1111.1320,
title = {The odd nilHecke algebra and its diagrammatics},
author = {Alexander P. Ellis and Mikhail Khovanov and Aaron D. Lauda},
journal= {arXiv preprint arXiv:1111.1320},
year = {2014}
}
Comments
48 pages, eps and xypic diagrams