Irreducible components of exotic Springer fibres
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Publication:4646249
DOI10.1112/JLMS.12152zbMATH Open1439.14137arXiv1611.05844OpenAlexW3122141731MaRDI QIDQ4646249
Neil Saunders, Vinoth Nandakumar, Daniele Rosso
Publication date: 11 January 2019
Published in: Journal of the London Mathematical Society (Search for Journal in Brave)
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 the exotic Springer fibre have dimension 2, and show that in those cases one obtains Hirzebruch surfaces.
Full work available at URL: https://arxiv.org/abs/1611.05844
Combinatorial aspects of representation theory (05E10) Grassmannians, Schubert varieties, flag manifolds (14M15) Classical groups (algebro-geometric aspects) (14L35)
Related Items (3)
Irreducible components of exotic Springer fibres. II: The exotic Robinson-Schensted algorithm ⋮ Exotic Springer fibers for orbits corresponding to one-row bipartitions ⋮ On total Springer representations for the symplectic Lie algebra in characteristic 2 and the exotic case
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