256 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
Effective dimension of finite semigroups
In this paper we discuss various aspects of the problem of determining the
minimal dimension of an injective linear representation of a finite semigroup
over a field. We outline some general techniques and results, and apply them to
numerous examples.Comment: To appear in J. Pure Appl. Al
Categorification of (induced) cell modules and the rough structure of generalized Verma modules
This paper presents categorifications of (right) cell modules and induced
cell modules for Hecke algebras of finite Weyl groups. In type we show that
these categorifications depend only on the isomorphism class of the cell
module, not on the cell itself. Our main application is multiplicity formulas
for parabolically induced modules over a reductive Lie algebra of type ,
which finally determines the so-called rough structure of generalized Verma
modules. On the way we present several categorification results and give the
positive answer to Kostant's problem from \cite{Jo} in many cases. We also give
a general setup of decategorification, precategorification and
categorification.Comment: 59 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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