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A topological
construction for all two-row Springer varieties
Heather M. Russell |
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Vol. 253 (2011), No. 1, 221–255
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Abstract |
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Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification, Khovanov provides a topological construction of (m,m) Springer varieties. Here we extend his construction to all two-row Springer varieties. Using the combinatorial and diagrammatic properties of this construction we provide a particularly useful homology basis and construct the Springer representation using this basis. We also provide a skein-theoretic formulation of the representation in this case. |
Keywords
two-row Springer variety, Springer representation,
noncrossing matchings, tangle homology
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Mathematical Subject Classification 2000
Primary: 20C30, 55N45, 57M25, 57M60
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Milestones
Received: 9 July 2010
Revised: 26 October 2010
Accepted: 27 November 2010
Published: 28 November 2011
Proposed: Darren Long
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Authors |
| Heather M. Russell | |
| Department of Mathematics University of Southern California 3620 South Vermont Avenue, KAP 108 Los Angeles, CA 90089-2532 United States |
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