Vol. 72, No. 2, 1977

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Algebraic automorphisms of algebraic groups with stable maximal tori

Sarah J. Gottlieb

Vol. 72 (1977), No. 2, 461–470
Abstract

Let T1 and T2 be maximal tori of a connected linear algebraic group G GL(n,κ), and suppose some (algebraic group) automorphism σ of G stabilizes both T1 and T2. Suppose further that σ also stabilizes two Borel subgroups, B1 and B2, of G. This paper is about the following natural questions:

  1. Are T1 and T2 conjugate by a σ-fixed point of G?
  2. Are B1 and B2 conjugate by a σ-fixed point of G?
  3. If Ti Bi, (i = 1,2), are the Ti and Bi respectively conjugate by a single σ-fixed point of G?
  4. Are at least T1 and T2 described in (3) above conjugate by a σ-fixed point of G?

Mathematical Subject Classification 2000
Primary: 20G99
Secondary: 14L99
Milestones
Received: 12 January 1977
Revised: 23 March 1977
Published: 1 October 1977
Authors
Sarah J. Gottlieb