25 citations · 70 across the 16 of their papers we have counts for
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The source operator method: an overview
Salem Ben Saïd, Jean-Louis Clerc, Khalid Koufany
This is an overview on the {source operator method} which leads to the construction of symmetry breaking differential operators (SBDO) in the context of tensor product of two princ…
Vector-valued holomorphic discrete series and the Laplace transform : an example
Jean-Louis Clerc
For T a Hermitian symmetric tube-type domain, a family ( ) C of holomorphic vector-valued representations is studied. The corresponding Wallach set is determined.…
Construction à la Ibukiyama of symmetry breaking differential operators, I
Jean-Louis Clerc
The construction of symmetry breaking differential operators, using invariant pluri-harmonic polynomials, due to T. Ibukiyama in the context of the Siegel upper half space, is exte…
Symmetry Breaking Differential Operators for Tensor Products of Spinorial Representations
Jean-Louis Clerc, Khalid Koufany
Let be a Clifford module for the complexified Clifford algebra , its dual, and be the corresponding representations o…
Rankin-Cohen brackets on tube-type domains
Jean-Louis Clerc
A new formula is obtained for the holomorphic bi-differential operators on tube-type domains which are associated to the decomposition of the tensor product of two scalar holomorph…
Symmetry breaking differential operators, the source operator and Rodrigues formulæ
Jean-Louis Clerc
A Rodrigues type formula is obtained for the symbols of the covariant bi-differential operators on a simple Jordan algebra.
Conformally covariant bi-differential operators for differential forms
Salem Ben Saïd, Jean-Louis Clerc, Khalid Koufany
The classical Rankin-Cohen brackets are bi-differential operators from into . They are covariant for the (diag…
Conformally covariant differential operators for the diagonal action of O(p, q) on real quadrics
Jean-Louis Clerc
Let be a real projective quadric, where and is a parabolic subgroup of . Let $\left(π_{λ,ε}, \mathcal{H}_{λ,ε}\right)_{ (λ,ε)\in \mathbb {C}\times \{\pm\}…
Conformally Covariant Bi-Differential Operators on a Simple Real Jordan Algebra
Salem Ben Said, Jean-Louis Clerc, Khalid Koufany
For a simple real Jordan algebra a family of bi-differential operators from to is constructed. These operators are cova…
Another Approach to Juhl's Conformally Covariant Differential Operators from to
Jean-Louis Clerc
A family of differential operators on the sphere is constructed. The operators are conformally covariant for the action of the subgroup of…
Covariant bi-differential operators on matrix space
jean-Louis Clerc
A family of bi-differential operators from $C^\infty\big(\Mat(m,\mathbb R)\times\Mat(m,\mathbb R)\big)$ into $C^\infty\big(\Mat(m,\mathbb R)\big)$ which are covariant for the proje…
Singular conformally invariant trilinear forms, II The higher multiplicity cases
Jean-Louis Clerc
Let be the sphere of dimension . Let be the scalar principle series of representations of the conformal group , realized on $\…
Singular conformally invariant trilinear forms, I Multiplicity one results
Jean-Louis Clerc
A normalized holomorphic family (depending on ) of conformally invariant trilinear forms on the sphere is studied. Its zero set is described. For…
Conformal covariance for the powers of the Dirac operator
Jean-Louis Clerc, Bent Ørsted
A new proof of the conformal covariance of the powers of the flat Dirac operator is obtained. The proof uses their relation with the Knapp-Stein intertwining operators for the spin…
Intertwining operators for the generalized principal series on symmetric R-spaces
Jean-Louis Clerc
Three questions about the intertwining operators for the generalized principal series on a symmetric R-space are solved : description of the functional kernel, both in the compact…
Singular conformally invariant trilinear forms and covariant differential operators on the sphere
Jean-Louis Clerc
Let be the conformal group acting on the dimensional sphere , and let be the spherical principal series. For generic values of $\b…
Conformally invariant trilinear forms on the sphere
Jean-Louis Clerc, Bent Orsted
To each complex number is associated a representation of the conformal group on (spherical principal series). For three values $λ…