Oddification of the cohomology of type A Springer varieties

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 identified with the corresponding Specht module of the Hecke algebra at q=-1.

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References in corpus (4)

• Derived equivalences for symmetric groups and sl\_2-categorification
• The odd nilHecke algebra and its diagrammatics
• Categorification of quantum Kac-Moody superalgebras
• An invariant of tangle cobordisms via subquotients of arc rings

Cited by in corpus (7)

• Hopf Algebras in Combinatorics
• 0-Hecke algebra action on the Stanley-Reisner ring of the Boolean algebra
• DG structures on odd categorified quantum sl(2)
• Categorical lifting of the Jones polynomial: a survey
• Real Springer fibers and odd arc algebras
• Not even Khovanov homology
• Spin nilHecke algebras of classical type