Quantum affine algebras, combinatorics of Young walls, and global bases.
Réduction de produits semi-directs et conjecture de Gel'fand et Kirillov
Relation between invertibility of Casimir operators and semisimplicity of quadratic Lie superalgebras.
Representation theory of Neveu-Schwarz and Ramond algebras II: Fock modules
In this article, we study the structure of Fock modules over super Virasoro algebras. As an application, we construct Bechi-Rouet–Stora–Tyutin type resolutions for super minimal models and their descendants.
Représentations de dimension finie de l’algèbre de Cherednik rationnelle
On donne une condition nécessaire et suffisante pour l’existence de modules de dimension finie sur l’algèbre de Cherednik rationnelle associée à un système de racines.
Représentations des algèbres de Lie résolubles
Représentations des groupes de Lie nilpotents
Representations of codimension one non-abelian nilradical Lie algebras.
Representations of solvable Lie algebras. II. Twisted group rings
Representations of the Lie ring over the ring of integers.
Restriction to Levi subalgebras and generalization of the category
The category of all modules over a reductive complex Lie algebra is wild, and therefore it is useful to study full subcategories. For instance, Bernstein, Gelfand and Gelfand introduced a category of modules which provides a natural setting for highest weight modules. In this paper, we define a family of categories which generalizes the BGG category, and we classify the simple modules for a subfamily. As a consequence, we show that some of the obtained categories are semisimple.
Rigidity of generalized Verma modules
We prove that generalized Verma modules induced from generic Gelfand-Zetlin modules, and generalized Verma modules associated with Enright-complete modules, are rigid. Their Loewy lengths and quotients of the unique Loewy filtrations are calculated for the regular block of the corresponding category 𝒪(𝔭,Λ).
Semiholonomic jets and induced modules in Cartan geometry calculus
The famous Erlangen Programme was coined by Felix Klein in 1872 as an algebraic approach allowing to incorporate fixed symmetry groups as the core ingredient for geometric analysis, seeing the chosen symmetries as intrinsic invariance of all objects and tools. This idea was broadened essentially by Elie Cartan in the beginning of the last century, and we may consider (curved) geometries as modelled over certain (flat) Klein’s models. The aim of this short survey is to explain carefully the basic...
Serre functors for Lie algebras and superalgebras
We propose a new realization, using Harish-Chandra bimodules, of the Serre functor for the BGG category associated to a semi-simple complex finite dimensional Lie algebra. We further show that our realization carries over to classical Lie superalgebras in many cases. Along the way we prove that category and its parabolic generalizations for classical Lie superalgebras are categories with full projective functors. As an application we prove that in many cases the endomorphism algebra of the basic...
S-functions and characters of Lie algebras and Lie groups
Singular Blocks of the Category O.
Singular localization of -modules and applications to representation theory
We prove a singular version of Beilinson–Bernstein localization for a complex semi-simple Lie algebra following ideas from the positive characteristic case settled by [BMR06]. We apply this theory to translation functors, singular blocks in the Bernstein–Gelfand–Gelfand category O and Whittaker modules.
Singular vectors corresponding to imaginary roots in verma modules over affine Lie algebras.
Some properties of generalized reduced Verma modules over -graded modular Lie superalgebras
We study some properties of generalized reduced Verma modules over -graded modular Lie superalgebras. Some properties of the generalized reduced Verma modules and coinduced modules are obtained. Moreover, invariant forms on the generalized reduced Verma modules are considered. In particular, for -graded modular Lie superalgebras of Cartan type we prove that generalized reduced Verma modules are isomorphic to mixed products of modules.
Spherical Functions and a q-Analogue of Kostant's Weight Multiplicity Formula.