Publication

Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block

Donna Testerman
2018
Journal Articles

Abstract

Let G be a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed field F of characteristic p >= 0, and let u is an element of G be a non-identity unipotent element. Let phi be a non-trivial irreducible representation of G. Then the Jordan normal form of phi(u) contains at most one non-trivial block if and only if G is of type G(2), u is a regular unipotent element and dim phi

Official source

https://infoscience.epfl.ch/entities/publication/4533e516-c0ee-4500-8e5b-796bbd8ea9b7

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Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block

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