Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nilpotent centralizers and Springer isomorphisms   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.

3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th