Delorme, Patrick Selfextensions de modules de Harish-Chandra et une question de I. M. Gelfand. (French) Zbl 0559.17007 Homologie, groupes Ext\(^ n\) représentations de longueur finie des groupes de Lie, Astérisque 124/125, 31-48 (1985). [For the entire collection see Zbl 0547.00015.] Let G be a semisimple group, and X an irreducible Harish-Chandra module for G. This paper is concerned with the possible self-extensions of X. It is shown that they are in some sense controlled by the self-extensions of a one-dimensional module over a nice commutative algebra (usually a polynomial algebra). For X a generic principal series for a complex group, this control is made into an explicit equivalence of categories, verifying a conjecture of Gelfand. Reviewer: D.Vogan Cited in 1 ReviewCited in 4 Documents MSC: 17B55 Homological methods in Lie (super)algebras 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) Keywords:semisimple group; irreducible Harish-Chandra module; self-extensions; complex group; conjecture of Gelfand PDF BibTeX XML