Abstract
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 U P 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 \( \left({U}_P\right)\overset{\sim }{\to }{U}_P \) 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 SL n ; SO n , and Sp2n , viewed in the usual way as subgroups of GL n or GL2n , such a Springer isomorphism can be given explicitly by the Artin–Hasse exponential series.
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SOBAJE, P. SPRINGER ISOMORPHISMS IN CHARACTERISTIC p . Transformation Groups 20, 1141–1153 (2015). https://doi.org/10.1007/s00031-015-9320-2
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DOI: https://doi.org/10.1007/s00031-015-9320-2