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A GRAPHICAL CALCULUS FOR 2-BLOCK SPALTENSTEIN VARIETIES

Published online by Cambridge University Press:  29 March 2012

GISA SCHÄFER
GISA SCHÄFER*
Affiliation:
University of Bonn, Mathematikzentrum, Endenicher Allee 60, 53115 Bonn, Germany e-mail: gschaefe@uni-bonn.de
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Abstract

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We generalise statements known about Springer fibres associated to nilpotents with two 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 that encodes their structure as iterated fibre bundles with ℂℙ1 as base spaces, and compute their cohomology. At the end, we present a connection with coloured cobordisms generalising the construction of Khovanov (M. Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101(3) (2000), 359–426) and Stroppel (C. Stroppel, Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology, Compositio Mathematica145(4) (2009), 954–992).

Keywords

Primary: 14M15Secondary: 17B1018D1016S38
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 54 , Issue 2 , May 2012 , pp. 449 - 477
Copyright
Copyright © Glasgow Mathematical Journal Trust 2012

References

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