On the Dynkin index of a principal $\mathfrak{sl}_2$-subalgebra
| dc.creator | Panyushev, Dmitri I. | |
| dc.date | 2009-03-02 | |
| dc.date.accessioned | 2026-07-07T12:48:33Z | |
| dc.date.available | 2026-07-07T12:48:33Z | |
| dc.description | Let $g$ be a simple Lie algebra over an algebraically closed field of characteristic zero. The goal of this note is to prove a closed formula for the Dynkin index of a principal $sl_2$-subalgebra of $g$. The key step in the proof uses the "strange formula" of Freudenthal--de Vries. As an application, we (1) compute the Dynkin index any simple $g$-module regarded as $sl_2$-module and (2) obtain an identity connecting the exponents of $g$ and the dual Coxeter numbers of both $g$ and the Langlands dual $g^\vee$. | |
| dc.description | 6 pages, to appear in "Advances in Math" | |
| dc.identifier | https://arxiv.org/abs/0903.0398 | |
| dc.identifier | http://arxiv.org/abs/0903.0398 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/222092 | |
| dc.subject | Representation Theory | |
| dc.subject | 17B20 | |
| dc.title | On the Dynkin index of a principal $\mathfrak{sl}_2$-subalgebra | |
| dc.type | text |