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 degree component of the odd cohomology of Springer varieties is identifiedwith the corresponding Specht module of the Hecke algebra at q = −1.
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The definitive version is available at: http://imrn.oxfordjournals.org/content/2014/17/4822.abstract
Lauda, Aaron D., and Heather M. Russell. "Oddification of the Cohomology of Type A Springer Varieties." International Mathematics Research Notices 2014, no. 17 (2013): 4822-4854. doi:10.1093/imrn/rnt098.
Russell, Heather M. and Lauda, Aaron D., "Oddification of the Cohomology of Type A Springer Varieties" (2013). Math and Computer Science Faculty Publications. 108.