Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 5 (2009), 062, 7 pages      arXiv:0906.2766

On the Moore Formula of Compact Nilmanifolds

Hatem Hamrouni
Department of Mathematics, Faculty of Sciences at Sfax, Route Soukra, B.P. 1171, 3000 Sfax, Tunisia

Received December 17, 2008, in final form June 04, 2009; Published online June 15, 2009

Let G be a connected and simply connected two-step nilpotent Lie group and Γ a lattice subgroup of G. 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 IndΓG(1). Extending then the Abelian case.

Key words: nilpotent Lie group; lattice subgroup; rational structure; unitary representation; Kirillov theory.

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