BENSON-RATCLIFF CONJECTURE ON SOLVABLE LIE GROUPS

BENSON-RATCLIFF CONJECTURE ON SOLVABLE LIE GROUPS

The paper deals with the invariant for unitary irreducible representation introduced by Benson and Ratcliff in [5]. We first focus on the study of this invariant for the class of reduced semi-direct product of nilpotent Lie algebras, which leads to a way of constructing families of counter-examples to the B-R conjecture, as well as identifying another class of r-step nilpotent Lie algebras for which the conjecture holds. Finally we extend the study of the B-R invariant of a coadjoint orbit of a nilpotent Lie group to the class of almost abelian solvable (non-nilpotent) Lie group ℝⁿ ⋊ ℝ.