## 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

### MathOverflow Questions:

Lusztig’s $$q$$-analog of weight multiplicity with product formula

### 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