Darstellungen auflösbarer Lie-p-Algebren.
Deformations of vector fields and canonical coordinates on coadjoint orbits.
Determination of the Interwining Operators for Holomorphically Induced Representations of SU (p,q).
Diamond representations of
In [6], there is a graphic description of any irreducible, finite dimensional module. This construction, called diamond representation is very simple and can be easily extended to the space of irreducible finite dimensional -modules.In the present work, we generalize this construction to . We show it is in fact a description of the reduced shape algebra, a quotient of the shape algebra of . The basis used in [6] is thus naturally parametrized with the so called quasi standard Young tableaux....
Dual pairs and Kostant-Sekiguchi correspondence. II. Classification of nilpotent elements
We classify the homogeneous nilpotent orbits in certain Lie color algebras and specialize the results to the setting of a real reductive dual pair. For any member of a dual pair, we prove the bijectivity of the two Kostant-Sekiguchi maps by straightforward argument. For a dual pair we determine the correspondence of the real orbits, the correspondence of the complex orbits and explain how these two relations behave under the Kostant-Sekiguchi maps. In particular we prove that for a dual pair in...
Dual vector fields ii: calculating the Jacobian
Given a Lie algebra with a chosen basis, the change of coordinates relating coordinates of the first and second kinds near the identity of the corresponding local group yields some remarkable vector fields and dual vector fields. One family of vector fields is dual to a representation of the Lie algebra acting on a Fock-type space. To this representation an abelian family of dual vector fields is associated. The exponential of these commuting operators acting on an appropriate vacuum yields the...