On irreducible sl (2, R) - modules and sl 2-triples.
On multiplicities of simple subquotients in generalized Verma modules
We reduce the problem on multiplicities of simple subquotients in an -stratified generalized Verma module to the analogous problem for classical Verma modules.
On representation theory of quantum groups at roots of unity
Irreducible representations of quantum groups (in Woronowicz’ approach) were classified in J.Wang, B.Parshall, Memoirs AMS 439 in the case of q being an odd root of unity. Here we find the irreducible representations for all roots of unity (also of an even degree), as well as describe “the diagonal part” of the tensor product of any two irreducible representations. An example of a not completely reducible representation is given. Non-existence of Haar functional is proved. The corresponding representations...
On representations of Lie algebras of a generalized Tavis-Cummings model.
On representations of restricted Lie superalgebras
Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type , the baby Verma modules are proved to be simple for any regular nilpotent -character and typical weight . Moreover, we obtain the dimension formulas for projective covers of simple modules with -characters of standard Levi form.
On the asymptotics of the number of p̅-core partitions of integers
On the basic representation of the affine Kac-Moody Lie algebras
On the characteristic polynomials of orbital varieties
On the classification of primitive ideals for complex classical Lie algebras, II
On the classification of primitive ideals for complex classical Lie algebras, I
On the classification of primitive ideals for complex classical Lie algebras, III
On the classification of the Lie algebras .
On the composition structure of the twisted Verma modules for
We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra , including the explicit structure of singular vectors for both and one of its Lie subalgebras , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as -modules on the Schubert cells in the full flag manifold for .
On the computation of Clebsch-Gordan coefficients and the dilation effect.
On the Demazure character formula
On the Demazure character formula II. Generic homologies
On the Enright-Varadarajan modules : a construction of the discrete series
On the minimal canonical realizations of the Lie algebra
On the stability of subgroup actions on certain quasihomogeneous -varieties.
On the structure of an ...-stratified generalized Verma module over Lie algebra sl(n, C).