✦ LIBER ✦
Kostant's Conjecture and the Geometry of Cartan Subalgebras in the Rank Two and Exceptional Cases
✍ Scribed by Mark R. Sepanski
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 331 KB
- Volume
- 182
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
This paper deals with certain aspects of a conjecture made by B. Kostant in 1983 Ž . relating the Coxeter number to the occurrence of the simple finite groups L 2, q in simple complex Lie groups. In particular, we examine how the conjecture gives rise to certain presentations of the Lie algebra as a sum of Cartan subalgebras for the rank two and exceptional cases. The presentations studied are those with invariant properties with respect to Kostant and Kac elements. The techniques also Ž . connect certain presentations of the q q 1 dimensional representations of L 2, q to certain properties of Jacobi sums.