Document Type
Article
Publication Date
7-1-2011
Publication Title
Mathematical Proceedings of the Cambridge Philosophical Society
Abstract
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 natural) combinatorial description, which we use to prove that the Springer representation on H*(Xn) is irreducible in each degree. We explicitly identify the Kazhdan-Lusztig basis for the irreducible representation of Sn corresponding to the partition (n/2, n/2).
Volume
151
Issue
1
First Page
59
Last Page
81
ISSN
03050041
Version
Author's Accepted Manuscript
Recommended Citation
Russell, Heather M. and Tymoczko, Julianna S., "Springer Representations on the Khovanov Springer Varieties" (2011). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/105