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Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Springer Representations On The Khovanov Springer Varieties, Heather M. Russell, Julianna Tymoczko
Department of Math & Statistics Faculty Publications
Springer varieties are studied because their cohomology carries a natural action of the symmetric group Sn and their top-dimensional cohomology is irreducible. In his work on tangle invariants, Khovanov constructed a family of Springer varieties Xn as subvarieties of the product of spheres (S2)n. We show that if Xn is embedded antipodally in (S2)n then the natural Sn-action on (S2)n induces an Sn-representation on the image of H*(Xn). This representation is the Springer representation. Our construction admits an elementary (and geometrically …