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 -