Book Review: Conjugacy classes in semisimple algebraic groups
نویسندگان
چکیده
منابع مشابه
Products of Conjugacy Classes in Finite and Algebraic Simple Groups
We prove the Arad–Herzog conjecture for various families of finite simple groups — if A and B are nontrivial conjugacy classes, then AB is not a conjugacy class. We also prove that if G is a finite simple group of Lie type and A and B are nontrivial conjugacy classes, either both semisimple or both unipotent, then AB is not a conjugacy class. We also prove a strong version of the Arad–Herzog co...
متن کاملReality Properties of Conjugacy Classes in Algebraic Groups
Let G be an algebraic group defined over a field k. We call g ∈ G real if g is conjugate to g−1 and g ∈ G(k) as k-real if g is real in G(k). An element g ∈ G is strongly real if ∃h ∈ G, h2 = 1 (i.e. h is an involution) such that hgh−1 = g−1. Clearly, strongly real elements are real and are product of two involutions. Let G be a connected adjoint semisimple group over a perfect field k, with −1 ...
متن کاملCellini's Descent Algebra and Semisimple Conjugacy Classes of Finite Groups of Lie Type
By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. We conjecture that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction o...
متن کاملCellini's Descent Algebra and Semisimple Conjugacy Classes of Nite Groups of Lie Type
By algebraic group theory, there is a map from the semisimple conjugacy classes of a nite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. We conjecture that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction of ...
متن کاملCellini's Descent Algebra, Dynamical Systems, and Semisimple Conjugacy Classes of Finite Groups of Lie Type
By algebraic group theory, there is a map from the semisimple conjugacy classes of a finite group of Lie type to the conjugacy classes of the Weyl group. Picking a semisimple class uniformly at random yields a probability measure on conjugacy classes of the Weyl group. We conjecture that this measure agrees with a second measure on conjugacy classes of the Weyl group induced by a construction o...
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ژورنال
عنوان ژورنال: Bulletin of the American Mathematical Society
سال: 1997
ISSN: 0273-0979
DOI: 10.1090/s0273-0979-97-00689-7