City Research Online

Irreducible components of exotic Springer fibres

Nandakumar, V., Rosso, D. & Saunders, N. ORCID: 0000-0001-9149-6141 (2018). Irreducible components of exotic Springer fibres. Journal of the London Mathematical Society, 98(3), pp. 609-637. doi: 10.1112/jlms.12152

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.

Publication Type: Article
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
T Technology > TA Engineering (General). Civil engineering (General)
Departments: School of Science & Technology
School of Science & Technology > Mathematics
SWORD Depositor:
[thumbnail of Exotic Springer Fibers_LMS Accepted ArXiv.pdf]
Preview
Text - Accepted Version
Download (481kB) | Preview

Export

Add to AnyAdd to TwitterAdd to FacebookAdd to LinkedinAdd to PinterestAdd to Email

Downloads

Downloads per month over past year

View more statistics

Actions (login required)

Admin Login Admin Login