16 citations · 99 across the 59 of their papers we have counts for
30 papers · 1 filter
Strong -rigidity of the Heisenberg groups
Ingrid Beltita, Daniel Beltita
We prove a strong rigidity property of the Heisenberg groups, that is, they can be distinguished from any other 1-connected Lie groups via their unitary dual spaces, in particular…
Invariant Hilbert spaces of distribution vectors in Lie group representations
Ingrid Beltita, Daniel Beltita
For every unitary irreducible representation of a Lie group we prove that the representation Hilbert space is the only nonzero invariant Hilbert space of distribution vectors.
Crowned Lie groups and nets of real subspaces
Daniel Beltita, Karl-Hermann Neeb
We introduce the notion of a complex crown domain for a connected Lie group , and we use analytic extensions of orbit maps of antiunitary representations to these domains to con…
On the regular representation of solvable Lie groups with open coadjoint quasi-orbits
Ingrid Beltita, Daniel Beltita
We obtain a Lie theoretic intrinsic characterization of the connected and simply connected solvable Lie groups whose regular representation is a factor representation. When this is…
Holomorphic extension of one-parameter operator groups
Daniel Beltita, Karl-Hermann Neeb
We study holomorphic extensions of one-parameter groups on locally convex spaces with a view to applications to KMS boundary conditions. In the first part we deal with analytic ext…
Continuous selection of Lagrangian subspaces
Ingrid Beltita, Daniel Beltita
We study continuous selections of the set-valued map that takes every skew-symmetric bilinear form on a vector space to its corresponding set of maximal isotropic subspaces. Applic…
Square-integrable representations and the coadjoint action of solvable Lie groups
Ingrid Beltita, Daniel Beltita
We characterize the square-integrable representations of (connected, simply connected) solvable Lie groups in terms of the generalized orbits of the coadjoint action. We prove that…
Coadjoint orbits in representation theory of pro-Lie groups
Daniel Beltita, Amel Zergane
We present a one-to-one correspondence between equivalence classes of unitary irreducible representations and coadjoint orbits for a class of pro-Lie groups including all connected…
Nonlinear oblique projections
Ingrid Beltita, Daniel Beltita
We construct nonlinear oblique projections along subalgebras of nilpotent Lie algebras in terms of the Baker-Campbell-Hausdorff multiplication. We prove that these nonlinear projec…
Berezin symbols on Lie groups
Ingrid Beltita, Daniel Beltita, Benjamin Cahen
In this paper we present a general framework for Berezin covariant symbols, and we discuss a few basic properties of the corresponding symbol map, with emphasis on its injectivity…
Amenability and representation theory of pro-Lie groups
Daniel Beltita, Amel Zergane
We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one…
-dynamical systems of solvable Lie groups
Ingrid Beltita, Daniel Beltita
In this paper we develop a groupoid approach to some basic topological properties of dual spaces of solvable Lie groups using suitable dynamical systems related to the coadjoint ac…
Transference for Banach space representations of nilpotent Lie groups. Part 1. Irreducible representations
Ingrid Beltita, Daniel Beltita, Jose E. Gale
We establish a general CCR (liminarity) property for uniformly bounded irreducible representations of nilpotent Lie groups on reflexive Banach spaces, extending the well known prop…
Representations of nilpotent Lie groups via measurable dynamical systems
Ingrid Beltita, Daniel Beltita
We study unitary representations associated to cocycles of measurable dynamical systems. Our main result establishes conditions on a cocycle, ensuring that ergodicity of the dynami…
On Wigner transforms in infinite dimensions
Ingrid Beltita, Daniel Beltita, Marius Mantoiu
We investigate the Schrödinger representations of certain infinite-dimensional Heisenberg groups, using their corresponding Wigner transforms.
Weyl-Pedersen calculus for some semidirect products of nilpotent Lie groups
Ingrid Beltita, Daniel Beltita, Mihai Pascu
For certain nilpotent real Lie groups constructed as semidirect products, algebras of invariant differential operators on some coadjoint orbits are used in the study of boundedness…
Moment convexity of solvable locally compact groups
Daniel Beltita, Mihai Nicolae
We introduce moment maps for continuous unitary representations of general topological groups. For solvable separable locally compact groups, we prove that the closure of the image…
Coadjoint orbits of stepwise square integrable representations
Ingrid Beltita, Daniel Beltita
Nilpotent Lie groups with stepwise square integrable representations were recently investigated by J.A.~Wolf. We give an alternative approach to these representations by relating t…
Contractions of Lie algebras with 2-dimensional generic coadjoint orbits
Daniel Beltita, Benjamin Cahen
We determine all the contractions within the class of finite-dimensional real Lie algebras whose coadjoint orbits have dimensions .
On Kirillov's lemma for nilpotent Lie algebras
Ingrid Beltita, Daniel Beltita
We establish a sharpening of Kirillov's lemma on nilpotent Lie algebras with 1-dimensional center and use it to study the structure of 3-step nilpotent Lie algebras.
On the differentiable vectors for contragredient representations
Ingrid Beltita, Daniel Beltita
We establish a few simple results on contragredient representations of Lie groups, with a view toward applications to the abstract characterization of some spaces of pseudo-differe…
Boundedness for Pseudo-Differential Calculus on Nilpotent Lie Groups
Ingrid Beltita, Daniel Beltita, Mihai Pascu
We survey a few results on the boundedness of operators arising from the Weyl-Pedersen calculus associated with irreducible representations of nilpotent Lie groups.
Linear connections for reproducing kernels on vector bundles
Daniel Beltita, José E. Galé
We construct a canonical correspondence from a wide class of reproducing kernels on infinite-dimensional Hermitian vector bundles to linear connections on these bundles. The linear…
Faithful representations of infinite-dimensional nilpotent Lie algebras
Ingrid Beltita, Daniel Beltita
For locally convex, nilpotent Lie algebras we construct faithful representations by nilpotent operators on a suitable locally convex space. In the special case of nilpotent Banach-…