2003/11/30 by Patrice Tauvel, Rupert W. T. Yu
Mathematics · #math.RT #msc:17B05 #msc:17B20
published as Annales de l'Institut Fourier, 54 (2004) 1793-1810 · This paper is written in French. There is an english abstract. This second version contains minor corrections
arxiv created 2004/02/05 · arxiv updated 2009/12/01
We give an upper bound for the index of certain Lie algebras, called of seaweed type, introduced by V. Dergachev, A. Kirillov and D. Panyushev. We deduce from this a conjecture of D. Panyushev stated in "Inductive formulas for the index of seaweed Lie algebra, Moscow Math. Journal (2001) 221-241". We conjecture that our upper bound gives in fact a formula for the index of such Lie algebras, and we prove it in certain cases. Finally, we obtain a result concerning the index of parabolic subalgebras of a semisimple Lie algebra.