TY - JOUR
T1 - SPRINGER ISOMORPHISMS IN CHARACTERISTIC p
AU - SOBAJE, PAUL
N1 - Publisher Copyright:
© 2015, Springer Science+Business Media New York.
PY - 2015/12/1
Y1 - 2015/12/1
N2 - Let G be a simple algebraic group over an algebraically closed field of characteristic p, and assume that p is a separably good prime for G. Let P be a parabolic subgroup whose unipotent radical UP has nilpotence class less than p. We show that there exists a particularly nice Springer isomorphism for G which restricts to a certain canonical isomorphism Lie UP→∼UP defined by J.-P. Serre. This answers a question raised both by G. McNinch in [M2], and by J. Carlson et. al in [CLN]. For the groups SLn; SOn, and Sp2n, viewed in the usual way as subgroups of GLn or GL2n, such a Springer isomorphism can be given explicitly by the Artin–Hasse exponential series.
AB - Let G be a simple algebraic group over an algebraically closed field of characteristic p, and assume that p is a separably good prime for G. Let P be a parabolic subgroup whose unipotent radical UP has nilpotence class less than p. We show that there exists a particularly nice Springer isomorphism for G which restricts to a certain canonical isomorphism Lie UP→∼UP defined by J.-P. Serre. This answers a question raised both by G. McNinch in [M2], and by J. Carlson et. al in [CLN]. For the groups SLn; SOn, and Sp2n, viewed in the usual way as subgroups of GLn or GL2n, such a Springer isomorphism can be given explicitly by the Artin–Hasse exponential series.
UR - http://www.scopus.com/inward/record.url?scp=84945450046&partnerID=8YFLogxK
U2 - 10.1007/s00031-015-9320-2
DO - 10.1007/s00031-015-9320-2
M3 - Article
AN - SCOPUS:84945450046
SN - 1083-4362
VL - 20
SP - 1141
EP - 1153
JO - Transformation Groups
JF - Transformation Groups
IS - 4
ER -