The finite dimension property of the irreducible representations of Noetherian -Lie algebras.
The F-method and a branching problem for generalized Verma modules associated to
The branching problem for a couple of non-compatible Lie algebras and their parabolic subalgebras applied to generalized Verma modules was recently discussed in [15]. In the present article, we employ the recently developed F-method, [10], [11] to the couple of non-compatible Lie algebras , and generalized conformal -Verma modules of scalar type. As a result, we classify the -singular vectors for this class of -modules.
The geometry of nilpotent coadjoint orbits of convex type in hermitian Lie algebras.
The Hurwitz determinants and the signatures of irreducible representations of simple real Lie algebras
The paper deals with the real classical Lie algebras and their finite dimensional irreducible representations. Signature formulae for Hermitian forms invariant relative to these representations are considered. It is possible to associate with the irreducible representation a Hurwitz matrix of special kind. So the calculation of the signatures is reduced to the calculation of Hurwitz determinants. Hence it is possible to use the Routh algorithm for the calculation.
The index of centralizers of elements of reductive Lie algebras.
The jacobian modules of a representation of a Lie algebra and geometry of commuting varieties
The Khovanov-Lauda 2-category and categorifications of a level two quantum representation.
The Kostant partition functions for twisted Kac-Moody algebras.
The Lie algebra cohomology of jets.
The minimal orbit in a simple Lie algebra and its associated maximal ideal
The -cohomology of representations with an infinitesimal character
The PBW filtration, Demazure modules and toroidal current algebras.
The socle filtration of a Verma module
The supports of simple modules over toroidal algebras.
Towards the Jantzen conjecture
Towards the Jantzen conjecture. II
Towards the Kazhdan-Lusztig conjecture
Twisted vertex representations of quantum affine algebras.
Unipotent representations and Dixmier algebras
Unitary representations of the Virasoro algebra and a conjecture of Kac