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 compute projective dimension of translated simple modules in the regular block of the
Bernstein–Gelfand–Gelfand category in terms of Kazhdan–Lusztig combinatorics. This …

We determine the Ringel duals for all blocks in the parabolic versions of the BGG category O
ℒ associated to a reductive finite-dimensional Lie algebra. In particular, we find that, contrary …

We investigate various ways to define an analog of Bernstein-Gelfand-Gelfand category O
for the nonsemisimple Takiff extension of the Lie algebra sl 2⁠. We describe Gabriel quivers …

We determine all values of the parameters for which the cell modules form a standard
system, for a class of cellular diagram algebras including partition, Brauer, walled Brauer …

We prove that the categories of Gelfand-Zeitlin modules of $\mathfrak {g}=\mathfrak {gl} _n $
and Whittaker modules associated with a semi-simple complex finite-dimensional algebra …

We study a version of the BGG category O for Dynkin Borel subalgebras of root-reductive Lie
algebras g, such as gl (\infty). We prove results about extension fullness and compute the …

The main focus of this paper is Bott–Borel–Weil (BBW) theory for basic classical Lie
superalgebras. We take a purely algebraic self-contained approach to the problem. A new …

Let G be a p-adic reductive group and g its Lie algebra. We construct a functor from the
extension closure of the Bernstein-Gelfand-Gelfand category O associated to g into the …

We prove uniqueness of the essential order for stratified algebras having simple preserving
duality, generalizing a recent result of Coulembier for quasi-hereditary algebras. We apply …