158 research outputs found
Covariant bi-differential operators on matrix space
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 projective action of the group
on \Mat(m,\mathbb R) is constructed, generalizing both the
\emph{transvectants} and the \emph{Rankin-Cohen brackets} (case )
Orbits of triples in the Shilov boundary of a bounded symmetric domain
Let be a bounded symmetric domain of tube type, its Shilov
boundary, and the neutral component of its group of biholomorphic
transforms. We classify the orbits of in the set
Singular conformally invariant trilinear forms and covariant differential operators on the sphere
Let be the conformal group acting on the dimensional
sphere , and let be the spherical
principal series. For generic values of in , there exits a (essentially
unique) trilinear form on which is invariant under
. Using
differential operators on the sphere which are covariant under the
conformal group , we construct new invariant trilinear forms
corresponding to singular values of . The family of
generic invariant trilinear forms depend meromorphically on the parameter
and the new forms are shown to be residues of this
family
Conformally Covariant Bi-Differential Operators on a Simple Real Jordan Algebra
For a simple real Jordan algebra a family of bi-differential operators
from to is constructed.
These operators are covariant under the rational action of the conformal group
of They generalize the classical {\em Rankin-Cohen} brackets (case
)
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