Classification of Harish-Chandra modules over the Virasoro Lie algebra.
Classification of irreducible weight modules
Let be a reductive Lie algebra and let be a Cartan subalgebra. A -module is called a weighted module if and only if , where each weight space is finite dimensional. The main result of the paper is the classification of all simple weight -modules. Further, we show that their characters can be deduced from characters of simple modules in category .
Classification of the simple modules of the quantum Weyl algebra and the quantum plane
Classification theorem on irreducible representations of the -deformed algebra .
Cohomologie des fibrés en droites sur les variétés magnifiques de rang minimal
Le théorème de Borel-Weil-Bott décrit la cohomologie des fibrés en droites sur les variétés de drapeaux. On généralise ici ce théorème à une plus grande classe de variétés projectives : les variétés magnifiques de rang minimal.
Combinatorial constructions of weight bases: the Gelfand-Tsetlin basis.
Combinatorics, superalgebras, invariant theory and representation theory.
Constructing homomorphisms between Verma modules.
Construction of BGG sequences for AHS structures
This paper gives a description of a method of direct construction of the BGG sequences of invariant operators on manifolds with AHS structures on the base of representation theoretical data of the Lie algebra defining the AHS structure. Several examples of the method are shown.
Constructions of representations of rank two semisimple Lie algebras with distributive lattices.
Continuation of unitary derived functor modules out of the canonical chamber
Contraction par Frobenius de -modules
Soit un groupe algébrique semi-simple simplement connexe défini sur un corps algébriquement clos de caractéristique positive. Nous donnons une nouvelle preuve de l’existence d’un scindage de Frobenius de la variété des drapeaux de ainsi que de la nature -équivariante de celui-ci. L’outil principal est un scindage de l’endomorphisme de Frobenius défini sur toute l’algèbre des distributions de qui permet de « détordre » la structure des -modules.
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...
Étude de certaines représentations induites d'un groupe de Lie résoluble exponentiel
Exact Borel subalgebras of quasi-heriditary algebras, I (with an appendix by Leonard Scott).