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Irreducible components of exotic Springer fibres

Irreducible components of exotic Springer fibres

Nandakumar, Vinoth, Rosso, Daniele and Saunders, Neil (2018) Irreducible components of exotic Springer fibres. Journal of the London Mathematical Society, 98 (3). pp. 609-637. ISSN 0024-6107 (Print), 1469-7750 (Online) (doi:https://doi.org/10.1112/jlms.12152)

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Abstract

Kato introduced the exotic nilpotent cone to be a substitute for the ordinary nilpotent cone of type C with cleaner properties. Here we describe the irreducible components of exotic Springer fibres (the fibres of the resolution of the exotic nilpotent cone), and prove that they are naturally in bijection with standard bitableaux. As a result, we deduce the existence of an exotic Robinson–Schensted bijection, which is a variant of the type C Robinson–Schensted bijection between pairs of same-shape standard bitableaux and elements of the Weyl group; this bijection is described explicitly in the sequel to this paper. Note that this is in contrast with ordinary type C Springer fibres, where the parametrisation of irreducible components, and the resulting geometric Robinson–Schensted bijection, are more complicated. As an application, we explicitly describe the structure in the special cases where the irreducible components of theexotic Springer fibre have dimension 2, and show that in those cases one obtains Hirzebruch surfaces.

Item Type: Article
Uncontrolled Keywords: Springer Correspondence, Springer fibre, exotic nilpotent cone, symplectic group, Robinson-Schenstend correspondence, Hirzebruch surface.
Subjects: Q Science > QA Mathematics
Faculty / Department / Research Group: Faculty of Architecture, Computing & Humanities
Faculty of Architecture, Computing & Humanities > Department of Mathematical Sciences
Last Modified: 08 Jan 2019 14:57
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: None
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/21069

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