Analogues of Kostant's ...-cohomology formulas for unitary highest weight modules.
Analogues of Weyl's formula for reduced enveloping algebras.
Annihilators and associated varieties of unitary highest weight modules
Annihilators of Verma modules for Kac-Moody algebras.
Bases des représentations des groupes simples complexes
Berechnung der Gelfand-Kirillov-Dimension bei induzierten Darstellungen.
Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras.
BGG diagrams for contact graded odd dimensional orthogonal geometries
BGG resolutions via configuration spaces
We study the blow-ups of configuration spaces. These spaces have a structure of what we call an Orlik–Solomon manifold; it allows us to compute the intersection cohomology of certain flat connections with logarithmic singularities using some Aomoto type complexes of logarithmic forms. Using this construction we realize geometrically the Bernstein–Gelfand–Gelfand resolution as an Aomoto complex.
Bigèbres de Lie, doubles et carrés
Calcolo della funzione di partizione di Kostant
Forniamo un calcolo esplicito della funzione di partizione di Kostant per algebre di Lie complesse di rango . La tecnica principale consiste nella riduzione a casi più semplici ed all'uso di funzioni generatrici.
Canonical bases for -modules of spherical monogenics in dimension 3
Spaces of homogeneous spherical monogenics in dimension 3 can be considered naturally as -modules. As finite-dimensional irreducible -modules, they have canonical bases which are, by construction, orthogonal. In this note, we show that these orthogonal bases form the Appell system and coincide with those constructed recently by S. Bock and K. Gürlebeck in [3]. Moreover, we obtain simple expressions of elements of these bases in terms of the Legendre polynomials.
Caractères d'algèbres de Lie finies
Categories of nonstandard highest weight modules for affine Lie algebras.
Category for quantum groups
In this paper we study the BGG-categories associated to quantum groups. We prove that many properties of the ordinary BGG-category for a semisimple complex Lie algebra carry over to the quantum case. Of particular interest is the case when is a complex root of unity. Here we prove a tensor decomposition for both simple modules, projective modules, and indecomposable tilting modules. Using the known Kazhdan-Lusztig conjectures for and for finite dimensional -modules we are able to determine...
Certaines représentations infinies des algèbres de Lie semi-simples
Characters of irreducible representations of simple Lie superalgebras.
Characters of Irreducible Representations of the Lie Algebra of Vector Fields on the Circle.
Characters of Irreducible Representations of the Virasoro Algebra.
Characters on the trivalent diagram algebra .