Oksana Yakimova

collaborators

4 papers

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…

math.RT2004★ 6 cited

The centralisers of nilpotent elements in classical Lie algebras

O. S. Yakimova

The index of a finite-dimensional Lie algebra $g$ is the minimum of dimensions of stabilisers $g_{α}$ of elements $α \in g^{*}$ . Let $g$ be a reductive Lie algebra and $z (x)$ a centrali…