DOI
10.1093/imrn/rnt098
Abstract
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.
Document Type
Post-print Article
Publication Date
2013
Publisher Statement
Copyright © 2013 Oxford University Press.
The definitive version is available at: http://imrn.oxfordjournals.org/content/2014/17/4822.abstract
DOI: 10.1093/imrn/rnt098
Full Citation:
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.
Recommended Citation
Russell, Heather M. and Lauda, Aaron D., "Oddification of the Cohomology of Type A Springer Varieties" (2013). Department of Math & Statistics Faculty Publications. 108.
https://scholarship.richmond.edu/mathcs-faculty-publications/108