Let $\mathfrak {A} $ be a finite-dimensional simple Lie algebra over the complex numbers. It
is shown that a module is complete (or relatively complete) in the sense of Enright if and only …

We prove that certain subcategories of, consisting of complete modules having a quasi-
Verma flag with respect to a Levi subalgebra, admit a combinatorial description similar to …

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 …

Let g be a complex semisimple Lie algebra, ba Cartan subalgebra, R= l)* the set of non-zero
roots, R+~ R a system of positive roots, B~ R+ a set of simple roots, 9= n+ Ob|-the triangular …

Let 9 be a complex semisimple Lie algebra. In ([8], Prop. 12) Duflo gave a remarkable sum
formula interrelating induced ideals. The main result of this paper provides a natural …

Let G be a finite‐dimensional semisimple Lie algebra over the complex numbers. Let A be
the finite‐dimensional algebra of a (regular or singular) block of the BGG‐category O. By …

We study Translation functors and Wall-Crossing functors on infinite dimensional
representations of a complex semisimple Lie algebra using ${\mathcal {D}} $-modules. This …

Highest weight categories arising in Lie theory are known to be associated with finite
dimensional quasi-hereditary algebras such as Schur algebras or blocks of category O. An …

This paper presents a technique based on elementary K-theory. It relies on the fact that K, for
a category of graded modules can be viewed as a Z [T, Tl] module for some variable T. In …

The 1lirkhof-f Witt theorem asserts that, under certain conditions on a Lie algebra: I1 (over a
commutative ring K), the graded algebra associated with the enveloping algebra of 52 is …