A brief survey of Kazhdan-Lusztig theory and related topics. (English) Zbl 0836.20060
Haboush, William J. (ed.) et al., Algebraic groups and their generalizations: classical methods. Summer Research Institute on algebraic groups and their generalizations, July 6-26, 1991, Pennsylvania State University, University Park, PA, USA. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 56, Pt. 1, 105-124 (1994).
The survey deals mainly with multiplicities of Verma modules, Kazhdan- Lusztig polynomials, the conjectures by Jantzen and Kazhdan-Lusztig about them, and the proofs of the conjectures. The author outlines in some detail his results on parabolic analogues and explicit calculation of the Kazhdan-Lusztig polynomials [see for instance J. Algebra 111, 483-506 (1987; Zbl 0656.22007) and Geom. Dedicata 36, 95-119 (1990; Zbl 0716.17015)]. A list of 160 references to relevant articles concludes the survey.
For the entire collection see [Zbl 0793.00018].
For the entire collection see [Zbl 0793.00018].
Reviewer: H.de Vries (Nijmegen)
MSC:
| 20G05 | Representation theory for linear algebraic groups |
| 22E47 | Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 20H15 | Other geometric groups, including crystallographic groups |
| 17B35 | Universal enveloping (super)algebras |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 14M15 | Grassmannians, Schubert varieties, flag manifolds |
