zbMATH — the first resource for mathematics

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

22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
Full Text: DOI Link EuDML arXiv