Linear representation theory of unitriangular matrix group over a finite field

This article is about the linear representation theory of the unitriangular matrix group of finite degree $$n$$ over a finite field. We denote the field size by $$q$$ and the underlying prime by $$p$$. Let $$r = \log_p q$$.

Other information about this family

 * Element structure of unitriangular matrix group over a finite field

Information about other families of maximal unipotent subgroups

 * Linear representation theory of maximal unipotent subgroup of symplectic group over a finite field

Listing of degrees
We denote the field size by $$q$$ and the underlying prime by $$p$$. Let $$r = \log_p q$$.

Partial sum values of squares of degrees
For visual clarity, we omit cells beyond the maximum degree of irreducible representation. As we see from the table below, each of the unitriangular matrix groups up to degree four is a finite group in which all partial sum values of squares of degrees of irreducible representations divide the order of the group. However, the unitriangular matrix groups of degree five and higher do not have this property.