This book originated from graduate topics courses given by the first author at Yale University
and at the University of California, Berkeley. Since then, the exposition has grown to include …

In recent years several constructions of generalized Harish-Chandra modules have been
given,[24],[26],[27],[28],[29], and a classification of such modules with generic minimal k-type …

We make a first step towards a classification of simple generalized Harish-Chandra modules
which are not Harish-Chandra modules or weight modules of finite type. For an arbitrary …

We construct a new analogue of the BGG category O for the infinite-dimensional Lie
algebras g= sl (∞), o (∞), sp (∞). A main difference with the categories studied in [9] and [2] …

This paper is a continuation of our work [PS2] in which we prove some general results about
simple (g, k)-modules with bounded k-multiplicities (or bounded simple (g, k)-modules). In …

Let g be a semisimple complex Lie algebra and k⊂ g be any algebraic subalgebra reductive
in g. For any simple finite dimensional k-module V, we construct simple (g, k)-modules M …

Let g be a reductive Lie algebra and k⊂g be a reductive in g subalgebra. A (g,k)-module M
is a g-module for which any element m∈ M is contained in a finite-dimensional k-submodule …

We study cohomological induction for a pair \left(g,k\right), g being an infinitedimensional
locally reductive Lie algebra and k⊂g being of the form k_0⊂C_g\left(k_0\right), where …

Let gg be a complex finite-dimensional semisimple Lie algebra and kk be any sl (2)-
subalgebra of g g. In this paper we prove an earlier conjecture by Penkov and Zuckerman …

We study the variety g (l) consisting of matrices x∈ gl (n, C) such that x and its n− 1 by n− 1
cutoff xn− 1 share exactly l eigenvalues, counted with multiplicity. We determine the …