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Singularities, character formulas, and a \(q\)-analog of weight multiplicities. (English) Zbl 0561.22013

Astérisque 101-102, 208-229 (1983).
The author gives an interpretation for the multiplicities of weights in a finite dimensional representations of a simple complex Lie algebra \({\mathfrak g}\) in terms of intersection cohomologies of Schubert varieties of the corresponding adjoint Lie group \(G\). The method, used in the paper, is the study of the Hecke algebra of the corresponding (“affine”) Coxeter group.
For the entire collection see [Zbl 0515.00021].
Reviewer: S.Prishchepionok

MSC:

17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
20C08 Hecke algebras and their representations
14M15 Grassmannians, Schubert varieties, flag manifolds
14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry