258 research outputs found
A twisted approach to Kostant's problem
We use Arkhipov's twisting functors to show that the universal enveloping
algebra of a semi-simple complex finite-dimensional Lie algebra surjects onto
the space of ad-finite endomorphisms of the simple highest weight module
, whose highest weight is associated (in the natural way) with a
subset of simple roots and a simple root in this subset. This is a new step
towards a complete answer to a classical question of Kostant. We also show how
one can use the twisting functors to reprove the classical results related to
this question.Comment: 16 page
Combinatorial Gelfand models for some semigroups and q-rook monoid algebras
Inspired by the results of [R. Adin, A. Postnikov, Y. Roichman, Combinatorial
Gelfand model, preprint math.RT arXiv:0709.3962], we propose combinatorial
Gelfand models for semigroup algebras of some finite semigroups, which include
the symmetric inverse semigroup, the dual symmetric inverse semigroup, the
maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and
the factor power of the symmetric group. Furthermore we extend the Gelfand
model for the semigroup algebras of the symmetric inverse semigroup to a
Gelfand model for the -rook monoid algebra.Comment: 14 page
Primitive ideals, twisting functors and star actions for classical Lie superalgebras
We study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov’s twisting functors on the BGG category O. The third topic addresses deformed orbits of the Weyl group. These take over the role of the usual Weyl group orbits for Lie algebras, in the study of primitive ideals and twisting functors for Lie superalgebras
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