On a Construction of Representations and a Problem of Enright.
On a theorem of E. Cartan
On affine Kac-Moody Lie algebras
On bounded generalized Harish-Chandra modules
Let be a complex reductive Lie algebra and be any reductive in subalgebra. We call a -module bounded if the -multiplicities of are uniformly bounded. In this paper we initiate a general study of simple bounded -modules. We prove a strong necessary condition for a subalgebra to be bounded (Corollary 4.6), i.e. to admit an infinite-dimensional simple bounded -module, and then establish a sufficient condition for a subalgebra to be bounded (Theorem 5.1). As a result we are able to...
On category for cyclotomic rational Cherednik algebras
We study equivalences for category of the rational Cherednik algebras of type : a highest weight equivalence between and for and an action of on an explicit non-empty Zariski open set of parameters ; a derived equivalence between and whenever and have integral difference; a highest weight equivalence between and a parabolic category for the general linear group, under a non-rationality assumption on the parameter . As a consequence, we confirm special cases of conjectures...
On characteristic identities for Lie algebras
On dimension formulas for representations.
On formal series and infinite products over Lie algebras.
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 .