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On semisimple classes and semisimple characters in finite reductive groups

Olivier Brunat (2012)

Annales de l’institut Fourier

In this article, we study the elements with disconnected centralizer in the Brauer complex associated to a simple algebraic group G defined over a finite field with corresponding Frobenius map F and derive the number of F -stable semisimple classes of G with disconnected centralizer when the order of the fundamental group has prime order. We also discuss extendibility of semisimple characters of the fixed point subgroup G F to their inertia group in the full automorphism group. As a consequence, we...

On systems of linear inequalities

Masami Fujimori (2003)

Bulletin de la Société Mathématique de France

We show in detail that the category of general Roth systems or the category of semi-stable systems of linear inequalities of slope zero is a neutral Tannakian category. On the way, we present a new proof of the semi-stability of the tensor product of semi-stable systems. The proof is based on a numerical criterion for a system of linear inequalities to be semi-stable.

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