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.
Copyright © 2011 Pacific Journal of Mathematics. This article first appeared in Pacific Journal of Mathematics 253:1 (2011), 221-255.
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Russell, Heather M. "A Topological Constructions for All Two-row Springer Varieties." Pacific Journal of Mathematics 253, no. 1 (2011): 221-255.