Displaying similar documents to “Representations of s ⁢ l q ⁢ 3 at the roots of unity”

The duality correspondence of infinitesimal characters

Tomasz Przebinda (1996)

Colloquium Mathematicae

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We determine the correspondence of infinitesimal characters of representations which occur in Howe's Duality Theorem. In the appendix we identify the lowest K-types, in the sense of Vogan, of the unitary highest weight representations of real reductive dual pairs with at least one member compact.

On a variant of Kazhdan's property (T) for subgroups of semisimple groups

Mohammed Bachir Bekka, Nicolas Louvet (1997)

Annales de l'institut Fourier

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Let Γ be an irreducible lattice in a product G of simple groups. Assume that G has a factor with property (T). We give a description of the topology in a neighbourhood of the trivial one dimensional representation of Γ in terms of the topology of the dual space G ^ of G . We use this result to give a new proof for the triviality of the first cohomology group of Γ with coefficients in a finite dimensional unitary representation.

Geometric study of the beta-integers for a Perron number and mathematical quasicrystals

Jean-Pierre Gazeau, Jean-Louis Verger-Gaugry (2004)

Journal de Théorie des Nombres de Bordeaux

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We investigate in a geometrical way the point sets of   ℝ   obtained by the   β -numeration that are the   β -integers   ℤ β ⊂ ℤ [ β ]   where   β   is a Perron number. We show that there exist two canonical cut-and-project schemes associated with the   β -numeration, allowing to lift up the   β -integers to some points of the lattice   ℤ m   ( m =   degree of   β ) lying about the dominant eigenspace of the companion matrix of   β  . When   β   is in particular a Pisot number, this framework gives another proof of the fact...