Characters of the unitriangular group and the Mackey method

Let U be the unitriangular group over a finite field. We consider an interesting class of irreducible complex characters of U, so-called characters of depth 2. This is a next natural step after characters of maximal and submaximal dimension, whose description is already known. We explicitly describe the support of a character of depth 2 by a system of defining algebraic equations. After that, we calculate the value of such a character on an element from the support. The main technical tool used in the proofs is the Mackey little group method for semidirect products. (c) 2025 Elsevier GmbH. All rights are reserved, including those for text and data mining, AI training, and similar technologies.