Characteristic cycles and wave front cycles of representations of reductive Lie groups. (English) Zbl 0960.22009

Schmid, Wilfried; Vilonen, Kari

Ann. Math. (2) 151, No. 3, 1071-1118 (2000).

The main result of this paper settles the conjecture of Barbasch-Vogan [cf. D. Vogan, Oral lectures at Bowdoin College, August, 1989]: For any irreducible admissible representation \(\pi\) of a linear reductive Lie group \(G_{\mathbf R}\), the associated cycle \(\text{Ass}(\pi)\) [attached to \(\pi \) in D. Vogan, Invent. Math. 48, 75-98 (1978; Zbl 0389.17002)] coincides with the wave front cycle \(WF(\pi)\) [attached to \(\pi \) in D. Barbasch and D. Vogan, J. Funct. Anal. 37, 27-55 (1980; Zbl 0436.22011)] via the Kostant-Sekiguchi correspondence.

Reviewer: Vladimir L. Popov (Moskva)

MSC:

22E45

Representations of Lie and linear algebraic groups over real fields: analytic methods

Keywords:

reductive group; representation; Cartan decomposition; nilpotent orbit; cycle

Citations:

Zbl 0436.22011; Zbl 0389.17002