Intertwining functors and irreducibility of standard Harish-Chandra sheaves. (English) Zbl 0760.22019

Miličić, Dragan

Harmonic analysis on reductive groups, Proc. Conf., Brunswick/ME (USA) 1989, Prog. Math. 101, 209-222 (1991).

[For the entire collection see Zbl 0742.00061.]
The author sketches a proof of an irreducibility criterion for standard Harish-Chandra sheaves, similar to the one in [B. Speh and D. A. Vogan jun., Acta Math. 145, 227-299 (1980; Zbl 0457.22011)]. This result is part of a joint article to be published as a sequel to [H. Hecht, D. Miličić, W. Schmidt, and J. A. Wolf, Invent. Math. 90, 297-332 (1987; Zbl 0699.22022)], by the same authors. The main idea of the proof consists of a reduction to the case of \(SL(2,\mathbb{C})\).

Reviewer: H.de Vries (Nijmegen)

MSC:

22E46	Semisimple Lie groups and their representations
22E47	Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)

Keywords:

sheaf of differential operators; category of coherent \({\mathcal D}\)-modules; irreducibility; Harish-Chandra sheaves