A topological construction for all two-row Springer varieties

Details A topological construction for all two-row Springer varieties A topological construction for all two-row Springer varieties

2010-07-05

arxiv.org/abs/1007.0611v2

Pacific J. Math, Vol. 253 (2011), No. 1, 221-255

Mathematics

Geometric Topology

27 pages, many figures

Scientific paper

Springer varieties appear in both geometric representation theory and knot theory. Motivated by knot theory and categorification Khovanov provides a topological construction of $(n/2, n/2)$ Springer varieties. We extend Khovanov's 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.

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