A graphical calculus for 2-block Spaltenstein varieties

Details A graphical calculus for 2-block Spaltenstein varieties A graphical calculus for 2-block Spaltenstein varieties

2012-02-28

arxiv.org/abs/1202.6247v1

Mathematics

Representation Theory

Final version to appear in Glasgow Math. Journal

Scientific paper

We generalise statements known about Springer fibres associated to nilpotents with 2 Jordan blocks to Spaltenstein varieties. We study the geometry of generalised irreducible components (i.e. Bialynicki-Birula cells) and their pairwise intersections. In particular we develop a graphical calculus which encodes their structure as iterated fibre bundles with CP^1 as base spaces and compute their cohomology. At the end we present a connection with coloured cobordisms generalising a construction of Khovanov and Stroppel.

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