Unitary Representations of Lattices of Free Nilpotent Lie Groups of Step-Two

2013/07/05 by Vignon Oussa, Oussa, Vignon
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #math.RT

paper · pdf · doi:10.48550/arxiv.1307.1624

arxiv created 2013/08/10 · arxiv updated 2013/08/13

Abstract

Using a theorem proved by Bekka and Driutti, we show that if \mathfrakf is a freely generated nilpotent Lie algebra of step-two, then almost every irreducible representation of the corresponding Lie group restricted to some lattice Γ is an irreducible representation of Γ if the dimension of the Lie algebra is odd. However, if the dimension of the Lie algebra is even, then almost every unitary irreducible representation of the Lie group restricted to Γ is reducible.

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