1433-5883
Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block
Testerman
Donna M.
Ecole Polytech Fed Lausanne, Stn 8, CH-1015 Lausanne, Switzerland
Zalesski
Alexandre E.
2018
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].
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