# Darstellungstheorietage and Nikolaus Conference 2013

Speaker: Richard Dipper (Stuttgart)

Title: Irreducible Constituents of Minimal Degree in Super Characters of the Finite Unitriangular Groups

Abstract: Let $$U$$ be the group of lower unitriangular $$n \times n$$-matrices over the field with $$q$$ elements. To determine the conjugacy classes of $$U$$ for all $$n$$ and $$q$$ is known to be a wild problem, even to count them is still unsolved in general. The super character theory introduced by Andre and refined by Yan gives an approximation to classifying the irreducible complex characters of $$U$$. For each super character there exists a combinatorially determined lower bound (a power of $$q$$) for the degrees of the irreducible $$U$$-characters occurring as constituent. We classify the super characters containing irreducible constituents of minimal degree and determine those.