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Front d'onde et propagation des singularités pour un vecteur-distribution

Dominique Manchon (1999)

Colloquium Mathematicae

We define the wave front set of a distribution vector of a unitary representation in terms of pseudo-differential-like operators [M2] for any real Lie group G. This refines the notion of wave front set of a representation introduced by R. Howe [Hw]. We give as an application a necessary condition so that a distribution vector remains a distribution vector for the restriction of the representation to a closed subgroup H, and we give a propagation of singularities theorem for distribution vectors.

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

Khalid Koufany, Bent Ørsted (1996)

Annales de l'institut Fourier

For the scalar holomorphic discrete series representations of SU ( 2 , 2 ) and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside SU ( 2 , 2 ) . We construct a Cayley transform between the Ol’shanskiĭ semigroup having U ( 1 , 1 ) as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for SU ( 2 , 2 ) . This allows calculating the composition series in terms of harmonic analysis on U ( 1 , 1 ) . In particular we show that the Ol’shanskiĭ Hardy space for U ( 1 , 1 ) is different...

Functoriality and the Inverse Galois problem II: groups of type B n and G 2

Chandrashekhar Khare, Michael Larsen, Gordan Savin (2010)

Annales de la faculté des sciences de Toulouse Mathématiques

This paper contains an application of Langlands’ functoriality principle to the following classical problem: which finite groups, in particular which simple groups appear as Galois groups over ? Let be a prime and t a positive integer. We show that that the finite simple groups of Lie type B n ( k ) = 3 D S O 2 n + 1 ( 𝔽 k ) d e r if 3 , 5 ( mod 8 ) and G 2 ( k ) appear as Galois groups over , for some k divisible by t . In particular, for each of the two Lie types and fixed we construct infinitely many Galois groups but we do not have a precise control...

𝔤 -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

A Lie version of Turaev’s G ¯ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a 𝔤 -quasi-Frobenius Lie algebra for 𝔤 a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra ( 𝔮 , β ) together with a left 𝔤 -module structure which acts on 𝔮 via derivations and for which β is 𝔤 -invariant. Geometrically, 𝔤 -quasi-Frobenius Lie algebras are the Lie algebra structures associated to symplectic...

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