On symmetric invariants of centralisers in reductive Lie algebras

dc.creatorPanyushev, D.
dc.creatorPremet, A.
dc.creatorYakimova, O.
dc.date2006-10-01
dc.date2006-12-13
dc.date.accessioned2026-07-07T06:43:11Z
dc.date.available2026-07-07T06:43:11Z
dc.descriptionLet $g_e$ 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.description49 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/math/0610049
dc.identifierhttp://arxiv.org/abs/math/0610049
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102316
dc.subjectRepresentation Theory
dc.subjectAlgebraic Geometry
dc.subject17B45, 14L24, 13A50
dc.titleOn symmetric invariants of centralisers in reductive Lie algebras
dc.typetext

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