zbMATH — the first resource for mathematics

Unipotent representations and derived functor modules. (English) Zbl 0810.22005
Eastwood, Michael (ed.) et al., The Penrose transform and analytic cohomology in representation theory. AMS-IMS-SIAM summer research conference, June 27 - July 3, 1992, South Hadley, MA, USA. Providence, RI: American Mathematical Society. Contemp. Math. 154, 225-238 (1993).
This paper constitutes a brief summary of the geometric approach to the Langlands classification of real reductive groups, as developed in the author’s work with J. Adams and D. Vogan [The Langlands Classification and Irreducible Characters for Real Reductive Groups, Birkhäuser (1992; Zbl 0756.22004)]. The basic emphasis is on the unipotent Arthur packets associated to (special unipotent) Arthur parameters $$\psi:\text{SL}(2,\mathbb{C}) \to{^ \vee G}$$. Here the packets are defined in terms of characteristic cycles for sheaves, and the conjectured character identities with respect to endoscopic groups are a consequence of Lefschetz type fixed-point theorems (of Goresky-MacPherson type). Various conjectures and relations between unipotent representations and derived functor modules are also discussed.
For the entire collection see [Zbl 0780.00026].
MSC:
 2.2e+47 Semisimple Lie groups and their representations 2.2e+48 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)