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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...

Functional calculus in weighted group algebras.

Jacek Dziubanski, Jean Ludwig, Carine Molitor-Braun (2004)

Revista Matemática Complutense

Let G be a compactly generated, locally compact group with polynomial growth and let ω be a weight on G. We look for general conditions on the weight which allow us to develop a functional calculus on a total part of L1(G,ω). This functional calculus is then used to study harmonic analysis properties of L1(G,ω), such as the Wiener property and Domar's theorem.

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 ℚ ? Let ℓ be a prime and t a positive integer. We show that that the finite simple groups of Lie type B n ( ℓ k ) = 3 D S O 2 n + 1 ( 𝔽 ℓ k ) d e r if ℓ ≡ 3 , 5 ( mod 8 ) and G 2 ( ℓ k ) appear as Galois groups over ℚ , for some k divisible by t . In particular, for each of the two Lie types and fixed ℓ 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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