This is the first textbook treatment of work leading to the landmark 1979 Kazhdan–Lusztig
Conjecture on characters of simple highest weight modules for a semisimple Lie algebra gg …

The purpose of this paper is to study categorifications of tensor products of finite-
dimensional modules for the quantum group for sl _2. The main categorification is obtained …

We describe Serre functors for (generalisations of) the category associated with a
semisimple complex Lie algebra. In our approach, projective-injective modules, that is …

We investigate certain singular categories of Harish-Chandra bimodules realized as the
category of $\mathfrak {p} $-presentable modules in the principal block of the Bernstein …

We give a description of Arkhipov's and (Joseph's and Deodhar-Mathieu's versions of)
Enright's endofunctors on the category associated with a fixed triangular decomposition of a …

We show that, for an arbitrary finite-dimensional quasi-reductive Lie superalgebra over
${\mathbb {C}} $ with a triangular decomposition and a character $\zeta $ of the nilpotent …

We extend Kostant's result on annihilator ideals of non-singular simple Whittaker modules
over Lie algebras to (possibly singular) simple Whittaker modules over Lie superalgebras …

We study the structure of generalized Verma modules over a semi-simple complex finite-
dimensional Lie algebra, which are induced from simple modules over a parabolic …

For a finite-dimensional Lie algebra over with a fixed Levi decomposition, where is
semisimple, we investigate-modules which decompose, as-modules, into a direct sum of …

We introduce a notion of a category with full projective functors. It encodes certain common
properties of categories appearing in representation theory of Lie groups, Lie algebras and …