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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

##### MSC:
 17B55 Homological methods in Lie (super)algebras 22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)