Automorphisms of Direct Products of Groups and Their Geometrie Realisations.
Automorphisms, Orbits, and Homogeneous Spaces of Non-Connected Lie Groups.
spaces and rectifiability for Carnot-Carathéodory metrics: an introduction
This paper is meant as a (short and partial) introduction to the study of the geometry of Carnot groups and, more generally, of Carnot-Carathéodory spaces associated with a family of Lipschitz continuous vector fields. My personal interest in this field goes back to a series of joint papers with E. Lanconelli, where this notion was exploited for the study of pointwise regularity of weak solutions to degenerate elliptic partial differential equations. As stated in the title, here we are mainly concerned...
Backward stochastic differential equations in a Lie group
Banach algebras associated with Laplacians on solvable Lie groups and injectivity of the Harish-Chandra transform
For any connected Lie group G and any Laplacian Λ = X²₁ + ⋯ + X²ₙ ∈ 𝔘𝔤 (X₁,...,Xₙ being a basis of 𝔤) one can define the commutant 𝔅 = 𝔅(Λ) of Λ in the convolution algebra ℒ¹(G) as well as the commutant ℭ(Λ) in the group C*-algebra C*(G). Both are involutive Banach algebras. We study these algebras in the case of a "distinguished Laplacian" on the "Iwasawa part AN" of a semisimple Lie group. One obtains a fairly good description of these algebras by objects derived from the semisimple group....
Banach-Hecke algebras and -adic Galois representations.
Banach-Lie algebras of compact operators
Barth-Lefschetz theorems for singular spaces.
Base change for Bernstein centers of depth zero principal series blocks
Let be an unramified group over a -adic field. This article introduces a base change homomorphism for Bernstein centers of depth-zero principal series blocks for and proves the corresponding base change fundamental lemma. This result is used in the approach to Shimura varieties with -level structure initiated by M. Rapoport and the author in [15].
Base d'ondelettes sur les groupes de Lie stratifiés
Basic conjugacy theorems for G2.
Bending deformations of complex hyperbolic surfaces.
Berezin quantization and holomorphic representations
Berezin transform for non-scalar holomorphic discrete series
Let be a Hermitian symmetric space of the non-compact type and let be a discrete series representation of which is holomorphically induced from a unitary irreducible representation of . In the paper [B. Cahen, Berezin quantization for holomorphic discrete series representations: the non-scalar case, Beiträge Algebra Geom., DOI 10.1007/s13366-011-0066-2], we have introduced a notion of complex-valued Berezin symbol for an operator acting on the space of . Here we study the corresponding...
Berezin--Toeplitz quantization on the Schwartz space of bounded symmetric domains.
Berezin-Weyl quantization for Cartan motion groups
We construct adapted Weyl correspondences for the unitary irreducible representations of the Cartan motion group of a noncompact semisimple Lie group by using the method introduced in [B. Cahen, Weyl quantization for semidirect products, Differential Geom. Appl. 25 (2007), 177--190].
Besov algebras on Lie groups of polynomial growth
We prove an algebra property under pointwise multiplication for Besov spaces defined on Lie groups of polynomial growth. When the setting is restricted to H-type groups, this algebra property is generalized to paraproduct estimates.
Besov spaces and function series on Lie groups
In the paper we investigate the absolute convergence in the sup-norm of Harish-Chandra's Fourier series of functions belonging to Besov spaces defined on non-compact connected Lie groups.
Beyond the classical Weyl and Colin de Verdière’s formulas for Schrödinger operators with polynomial magnetic and electric fields
We present a pair of conjectural formulas that compute the leading term of the spectral asymptotics of a Schrödinger operator on with quasi-homogeneous polynomial magnetic and electric fields. The construction is based on the orbit method due to Kirillov. It makes sense for any nilpotent Lie algebra and is related to the geometry of coadjoint orbits, as well as to the growth properties of certain “algebraic integrals,” studied by Nilsson. By using the direct variational method, we prove that the...
BGG sequences on spheres
BGG sequences on flat homogeneous spaces are analyzed from the point of view of decomposition of appropriate representation spaces on irreducible parts with respect to a maximal compact subgroup, the so called -types. In particular, the kernels and images of all standard invariant differential operators (including the higher spin analogs of the basic twistor operator), i.e. operators appearing in BGG sequences, are described.