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A proof of Jantzen conjectures. (English) Zbl 0790.22007
Gelfand, Sergej (ed.) et al., I. M. Gelfand Seminar. Part 1: Papers of the Gelfand seminar in functional analysis held at Moscow University, Russia, September 1993. Providence, RI: American Mathematical Society. Adv. Sov. Math. 16(1), 1-50 (1993).
It is shown that the localization functor sends the Jantzen filtration on standard Harish-Chandra modules to the weight filtration on the corresponding perverse sheaves. The fact implies, conjectured by Jantzen, the hereditary property of the Jantzen filtration, the socle and cosocle properties, and so on.
For the entire collection see [Zbl 0777.00035].

22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
14F43 Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies)