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].
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 |
