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The characteristic cycles of holonomic systems on a flag manifold related to the Weyl group algebra. (English) Zbl 0611.22008
The authors give a relation between the characteristic cycles of the holonomic systems on G/B entering into the proof of the Kazhdan-Lusztig conjecture and the Springer representations of the Weyl group: W operates on the K-group of the holonomic systems: \(w\cdot [{\mathfrak M}_ y]=[{\mathfrak M}_{wy}]\) for \(w\in W\) (\({\mathfrak M}_ w\) is the holonomic system corresponding to the Verma module with highest weight -w(\(\rho)\)-\(\rho)\); W operates on top-degree cycles on the conormal variety of the Schubert cells by a representation constructed by Kazhdan-Lusztig in connection with the Springer representation. The main result of the paper is equivalent to the assertion that the map which associates to each holonomic system its characteristic cycle is a W-isomorphism for these W- actions.
Reviewer: W.Rossmann

MSC:
22E46 Semisimple Lie groups and their representations
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
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