Affine pavings and the enhanced nilpotent cone

Mautner, Carl

doi:10.1090/proc/13329

Affine pavings and the enhanced nilpotent cone
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Proc. Amer. Math. Soc. 145 (2017), 1393-1398 Request permission

Abstract:

We construct affine pavings of Springer-type fibers over the enhanced nilpotent cone. This resolves a question of Achar-Henderson and implies the existence of perverse parity sheaves on the enhanced nilpotent cone.

References

Pramod N. Achar and Anthony Henderson, Orbit closures in the enhanced nilpotent cone, Adv. Math. 219 (2008), no. 1, 27–62. MR 2435419, DOI 10.1016/j.aim.2008.04.008
Pramod N. Achar and Anthony Henderson, Corrigendum to “Orbit closures in the enhanced nilpotent cone” [Adv. Math. 219 (1) (2008) 27–62] [MR2435419], Adv. Math. 228 (2011), no. 5, 2984–2988. MR 2838068, DOI 10.1016/j.aim.2011.05.030
C. De Concini, G. Lusztig, and C. Procesi, Homology of the zero-set of a nilpotent vector field on a flag manifold, J. Amer. Math. Soc. 1 (1988), no. 1, 15–34. MR 924700, DOI 10.1090/S0894-0347-1988-0924700-2
Birger Iversen, A fixed point formula for action of tori on algebraic varieties, Invent. Math. 16 (1972), 229–236. MR 299608, DOI 10.1007/BF01425495
Jens Carsten Jantzen, Nilpotent orbits in representation theory, Lie theory, Progr. Math., vol. 228, Birkhäuser Boston, Boston, MA, 2004, pp. 1–211. MR 2042689
Daniel Juteau, Carl Mautner, and Geordie Williamson, Parity sheaves, J. Amer. Math. Soc. 27 (2014), no. 4, 1169–1212. MR 3230821, DOI 10.1090/S0894-0347-2014-00804-3
Michael Sun, Point stabilisers for the enhanced and exotic nilpotent cones, J. Group Theory 14 (2011), no. 6, 825–839. MR 2855780, DOI 10.1515/JGT.2010.080
Roman Travkin, Mirabolic Robinson-Schensted-Knuth correspondence, Selecta Math. (N.S.) 14 (2009), no. 3-4, 727–758. MR 2511197, DOI 10.1007/s00029-009-0508-y