ODDIFICATION OF THE COHOMOLOGY OF TYPE A SPRINGER VARIETIES

@article{Lauda2014ODDIFICATIONOT,
  title={ODDIFICATION OF THE COHOMOLOGY OF TYPE A SPRINGER VARIETIES},
  author={Aaron D. Lauda and Heather M. Russell},
  journal={International Mathematics Research Notices},
  year={2014},
  volume={2014},
  pages={4822-4854}
}
We identify the ring of odd symmetric functions introduced by Ellis and Khovanov as the space of skew polynomials fixed by a natural action of the Hecke algebra at q = 1. This allows us to define graded modules over the Hecke algebra at q = 1 that are 'odd' analogs of the cohomology of type A Springer varieties. The graded module associated to the full flag variety corresponds to the quotient of the skew polynomial ring by the left ideal of nonconstant odd symmetric functions. The top… 

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