-adic Teichmüller space and Siegel halfspace
Pluriharmonic functions on symmetric tube domains with BMO boundary values
Let 𝓓 be a symmetric Siegel domain of tube type and S be a solvable Lie group acting simply transitively on 𝓓. Assume that L is a real S-invariant second order operator that satisfies Hörmander's condition and annihilates holomorphic functions. Let H be the Laplace-Beltrami operator for the product of upper half planes imbedded in 𝓓. We prove that if F is an L-Poisson integral of a BMO function and HF = 0 then F is pluriharmonic. Some other related results are also considered.
Pointwise convergent nets of holomorphic automorphisms of the unit ball of Cartan factors.
Polynomially growing pluriharmonic functions on Siegel domains
Let 𝓓 be a symmetric type two Siegel domain over the cone of positive definite Hermitian matrices and let N(Φ)S be a solvable Lie group acting simply transitively on 𝓓. We characterize polynomially growing pluriharmonic functions on 𝓓 by means of three N(Φ)S-invariant second order elliptic degenerate operators.
Radial limits of the Poisson kernel on the classical Cartan domains
Reflections in bounded symmetric domains
Relative discrete series of line bundles over bounded symmetric domains
We study the relative discrete series of the -space of the sections of a line bundle over a bounded symmetric domain. We prove that all the discrete series appear as irreducible submodules of the tensor product of a holomorphic discrete series with a finite dimensional representation.
Reproducing properties and -estimates for Bergman projections in Siegel domains of type II
On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space .
Rigidity of convex realizations of irreducible bounded symmetric domains of rank ...2.
Satake Compactification and Extension of Holomorphic Mappings.
Semi-groupe de Lie associé à un cône symétrique
Soit une algèbre de Jordan simple euclidienne de dimension finie et le cône symétrique associé. Nous étudions dans cet article le semi-groupe , naturellement associé à , formé des automorphismes holomorphes du domaine tube qui appliquent le cône dans lui-même.
Separately radial and radial Toeplitz operators on the projective space and representation theory
We consider separately radial (with corresponding group ) and radial (with corresponding group symbols on the projective space , as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the -algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the...
Stratonovich-Weyl correspondence for discrete series representations
Let be a Hermitian symmetric space of the noncompact type and let be a discrete series representation of holomorphically induced from a unitary character of . Following an idea of Figueroa, Gracia-Bondìa and Vàrilly, we construct a Stratonovich-Weyl correspondence for the triple by a suitable modification of the Berezin calculus on . We extend the corresponding Berezin transform to a class of functions on which contains the Berezin symbol of for in the Lie algebra of . This allows...
Stratonovich-Weyl correspondence for the Jacobi group
We construct and study a Stratonovich-Weyl correspondence for the holomorphic representations of the Jacobi group.
Sur la décomposition d'un domaine borné symétrique en produit continu de domaines bornés symétriques irréductibles
Sur la division des domaines de Siegel
Sur la simplification dans les isomorphismes analytiques
Sur la valeur au bord du noyau de Poisson d'un domaine borné symétrique.
Sur les équations d'Halphen et les actions de SL2(C)
On étudie les aspects locaux et globaux des actions holomorphes de SL2(C) sur les variétés complexes de dimension trois, à partir de l’étude des algèbres de Lie de champs de vecteurs qui engendrent une action uniforme. On décrit géométriquement et dynamiquement une famille de telles algèbres étudiée par Halphen vers la fin du XIXème siècle. On donne des formes normales pour les actions de SL2(C) au voisinage des orbites unidimensionnelles. On étudie ensuite les compactifications équivariantes des...
Symmetry and local conjugacy on complex manifolds.