Oksana Yakimova

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math.RT2006

On symmetric invariants of centralisers in reductive Lie algebras

D. Panyushev, A. Premet, O. Yakimova

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 invest…

math.RT2005

(Ir)Reducibility of some commuting varieties associated with involutions

Oksana Yakimova

Here we prove that a commuting variety associated with a symmetric pair (g, g_0) is irreducible for (so_{n+m}, so_n + so_m) and reducible for (gl_{n+m}, {gl}_n + gl_m) with n>m, (s…

math.RT2005

The index of representations associated with stabilisers

Dmitri I. Panyushev, Oksana S. Yakimova

Let $Q$ be an algebraic group and $V$ a $Q$ -module. The index of $V$ is the minimal codimension of the $Q$ -orbits in the dual space $V^{*}$ . There is a general inequality, due to Vin…