Representations of Gelfand-Graev type for the unitriangular group

TL;DR

This paper studies Gelfand-Graev type representations for the unitriangular group, decomposing them into irreducibles, proving multiplicity freeness, and calculating the associated Hecke algebra.

Contribution

It introduces Gelfand-Graev analogs for the uniteriangular group and provides their explicit decomposition and algebraic properties.

Findings

Decomposition into irreducible representations

Proven multiplicity freeness of these representations

Calculated the associated Hecke algebra

Abstract

We consider the analog of Gelfand-Graev representations of the uniteriangular group. We obtain the decomposition into the sum of irreducible representations, prove that these representations are multiplicity free, calculate the Hecke algebra.}