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

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 <= 7. Note that the irreducible representations of the simple classical algebraic groups in which a non-trivial unipotent element is represented by a matrix whose Jordan form has a single non-trivial block were determined by I. D. Suprunenko [21].


Publié dans:
Journal Of Group Theory, 21, 1, 1-20
Année
2018
Publisher:
Berlin, Walter De Gruyter Gmbh
ISSN:
1433-5883
Laboratoires:




 Notice créée le 2018-01-15, modifiée le 2018-12-03


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