| Title:
|
A simple construction of basic polynomials invariant under the Weyl group of the simple finite-dimensional complex Lie algebra (English) |
| Author:
|
Perelomov, Askold M. |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
28 |
| Issue:
|
3 |
| Year:
|
2020 |
| Pages:
|
301-305 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For every simple finite-dimensional complex Lie algebra, I give a simple construction of all (except for the Pfaffian) basic polynomials invariant under the Weyl group. The answer is given in terms of the two basic polynomials of smallest degree. (English) |
| Keyword:
|
Weyl group |
| Keyword:
|
invariant polynomial |
| MSC:
|
11F22 |
| idZBL:
|
Zbl 07426513 |
| idMR:
|
MR4197081 |
| . |
| Date available:
|
2021-03-03T09:00:31Z |
| Last updated:
|
2022-04-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148710 |
| . |
| Reference:
|
[1] Chevalley, C.: Invariants of finite groups generated by reflections.American Journal of Mathematics, 77, 4, 1955, 778-782, JSTOR, MR 0072877, 10.2307/2372597 |
| Reference:
|
[2] Kostant, B.: The principal three-dimensional subgroup and the Betti numbers of a complex simple Lie group.American Journal of Mathematics, 81, 1959, 973-1032, MR 0114875, 10.2307/2372999 |
| Reference:
|
[3] Macdonald, I.G.: Orthogonal polynomials associated with root systems.Séminaire Lotharingien de Combinatoire, 45, 2000, B45a, MR 1817334 |
| Reference:
|
[4] Mehta, M.L.: Basic sets of invariant polynomials for finite reflection groups.Communications in Algebra, 16, 5, 1988, 1083-1098, Taylor & Francis, MR 0926338, 10.1080/00927878808823619 |
| Reference:
|
[5] Onishchik, A.L., Vinberg, E.B.: Lie groups and algebraic groups.1990, Springer, MR 1064110 |
| Reference:
|
[6] Racah, G.: Sulla caratterizzazione delle rappresentazioni irriducibili dei gruppi semisemplici di Lie.Lincei-Rend. Sc. fis. mat. e nat, 8, 1950, 108-112, MR 0035771 |
| Reference:
|
[7] Witt, E.: Spiegelungsgruppen und aufz{ä}hlung halbeinfacher liescher Ringe.Abhandlungen aus dem mathematischen Seminar der Universit{ä}t Hamburg, 14, 1, 1941, 289-322, Springer, MR 0005099 |
| . |
