Nilpotent centralizers and Springer isomorphisms
| dc.creator | McNinch, George | |
| dc.creator | Testerman, Donna | |
| dc.date | 2008-05-16 | |
| dc.date | 2008-12-10 | |
| dc.date.accessioned | 2026-07-07T12:10:32Z | |
| dc.date.available | 2026-07-07T12:10:32Z | |
| dc.description | Let G be a semisimple algebraic group over a field K whose characteristic is very good for G, and let sigma be any G-equivariant isomorphism from the nilpotent variety to the unipotent variety; the map sigma is known as a Springer isomorphism. Let y in G(K), let Y in Lie(G)(K), and write C_y = C_G(y) and C_Y= C_G(Y) for the centralizers. We show that the center of C_y and the center of C_Y are smooth group schemes over K. The existence of a Springer isomorphism is used to treat the crucial cases where y is unipotent and where Y is nilpotent. Now suppose G to be quasisplit, and write C for the centralizer of a rational regular nilpotent element. We obtain a description of the normalizer N_G(C) of C, and we show that the automorphism of Lie(C) determined by the differential of sigma at zero is a scalar multiple of the identity; these results verify observations of J-P. Serre. | |
| dc.description | New version reflects a few suggestions made by a referee. To appear: J. Pure and Applied Algebra | |
| dc.identifier | https://arxiv.org/abs/0805.2574 | |
| dc.identifier | http://arxiv.org/abs/0805.2574 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209960 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Group Theory | |
| dc.subject | 20G15 | |
| dc.title | Nilpotent centralizers and Springer isomorphisms | |
| dc.type | text |