From a topological theory of semigroup to a geometric one.
From double Lie groups to quantum groups
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
Front d'onde et propagation des singularités pour un vecteur-distribution
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 and fixed point properties: a Galois connection.
Function spaces on semitopological semigroups.
Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program
For the scalar holomorphic discrete series representations of and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside . We construct a Cayley transform between the Ol’shanskiĭ semigroup having as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for . This allows calculating the composition series in terms of harmonic analysis on . In particular we show that the Ol’shanskiĭ Hardy space for is different...
Functional calculus in weighted group algebras.
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.
Functional calculus of Lie groups and wave propagation.
Functional equation satisfied by certain -functions
Functional equations and *-representations on topological semigroups.
Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups
Functions of Translation Type and Functorial Properties of Segal Algebras II.
Functions on the universal cover of the prinicpal nilpotent orbit.
Functions with a Finite Number of Negative Squares on Semigroups.
Functorial prolongations of Lie groups and their actions
Functoriality and the Inverse Galois problem II: groups of type and
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 a positive integer. We show that that the finite simple groups of Lie type if and appear as Galois groups over , for some divisible by . 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...
Functoriality for the classical groups
Fundamental solutions for translation and rotation invariant differential operators on the Heisenberg group
Fundamental solutions of differential operators on homogeneous manifolds of negative curvature and related Riesz transforms
Fundamental vector fields on associated fiber bundles