On symmetric invariants of centralisers in reductive Lie algebras
| dc.creator | Panyushev, D. | |
| dc.creator | Premet, A. | |
| dc.creator | Yakimova, O. | |
| dc.date | 2006-10-01 | |
| dc.date | 2006-12-13 | |
| dc.date.accessioned | 2026-07-07T06:43:11Z | |
| dc.date.available | 2026-07-07T06:43:11Z | |
| dc.description | Let $g_e$ be the centraliser of a nilpotent element $e$ in a finite dimensional simple Lie algebra $g$ of rank $l$ over an algebraically closed field of characteristic 0. We investigate the algebra $S(g_e)^{g_e}$ of symmetric invariants of $g_e$ and prove that if $g$ is of type $A$ or $C$, then $S(g_e)^{g_e}$ is always a graded polynomial algebra in $l$ variables. We show that this continues to hold for some nilpotent elements in the Lie algebras of other types. In type $A$ we prove that $S(g_e)^{g_e}$ is freely generated by a regular sequence in $S(g_e)$ and describe the tangent cone at $e$ to the nilpotent variety of $g$. | |
| dc.description | 49 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0610049 | |
| dc.identifier | http://arxiv.org/abs/math/0610049 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/102316 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 17B45, 14L24, 13A50 | |
| dc.title | On symmetric invariants of centralisers in reductive Lie algebras | |
| dc.type | text |