Reduction of structure to parabolic subgroups

  • Danny Ofek

    Department of Mathematics, University of British Columbia, 1984 Mathematics Rd, Vancouver, BC V6T 1Z2, Canada
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Let GG be an affine group over a field of characteristic not two. A GG-torsor is called isotropic if it admits reduction of structure to a proper parabolic subgroup of GG. This definition generalizes isotropy of affine groups and involutions of central simple algebras. When does GG admit anisotropic torsors? Building on work of J. Tits, we answer this question for simple groups. We also give an answer for connected and semisimple GG under certain restrictions on its root system.

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Danny Ofek, Reduction of structure to parabolic subgroups. Doc. Math. 27 (2022), pp. 1421–1446

DOI 10.4171/DM/901