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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.

##### MSC:
 2.2e+46 Representations of Lie and linear algebraic groups over real fields: analytic methods
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