
TL;DR
This paper presents a new multiplicity formula for irreducible unitary representations in the decomposition of quasi-regular representations of two-step nilpotent Lie groups, extending Moore's formula from the Abelian case.
Contribution
It introduces a novel multiplicity formula for the decomposition of quasi-regular representations of two-step nilpotent Lie groups, generalizing Moore's formula beyond Abelian groups.
Findings
New multiplicity formula for two-step nilpotent Lie groups
Extension of Moore's formula from Abelian to non-Abelian cases
Enhanced understanding of representation decomposition in nilmanifolds
Abstract
Let be a connected and simply connected two-step nilpotent Lie group and a lattice subgroup of . In this note, we give a new multiplicity formula, according to the sense of Moore, of irreducible unitary representations involved in the decomposition of the quasi-regular representation . Extending then the Abelian case.
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