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• W3048952384 abstract "We prove the following extension of Tits’ simplicity theorem. Let $$k$$ be an infinite field, G an algebraic group defined and quasi-simple over $$k,$$ and $$G(k)$$ the group of $$k$$ -rational points of G. Let $$G(k)^+$$ be the subgroup of $$G(k)$$ generated by the unipotent radicals of parabolic subgroups of G defined over $$k$$ and denote by $$PG(k)^+$$ the quotient of $$G(k)^+$$ by its center. Then every normalized function of positive type on $$PG(k)^+$$ which is constant on conjugacy classes is a convex combination of $$mathbf {1}_{PG(k)^+}$$ and $$delta _e.$$ As corollary, we obtain that, when $$k$$ is countable, the only ergodic IRS’s (invariant random subgroups) of $$PG(k)^+$$ are $$delta _{PG(k)^+}$$ and $$delta _{{e}}.$$ A further consequence is that, when $$k$$ is a global field and G is $$k$$ -isotropic and has trivial center, every measure preserving ergodic action of $$G(k)$$ on a probability space either factorizes through the abelianization $$G(k)_{mathrm{ab}}$$ or is essentially free." @default.
• W3048952384 created "2020-08-18" @default.
• W3048952384 creator A5003113893 @default.
• W3048952384 date "2020-08-12" @default.
• W3048952384 modified "2023-10-16" @default.
• W3048952384 title "Character rigidity of simple algebraic groups" @default.
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• W3048952384 doi "https://doi.org/10.1007/s00208-020-02061-x" @default.
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