Alexey Boyarsky

The method is proposed of the explicit embedding of the some types of the singular orbits of the adjoint action of the some classical Lie groups in the corresponding (co)algebras as the level surfaces of the special polynomials. In fact, orbits of types $SO(2n)/SO(2k) \times SO(2)^{n-k}$, $SO(2n+1)/SO(2k+1) \times SO(2)^{n-k}$, $E(2n-1)/R \times SO(2k) \times SO(2)^{n-k-1}$, $E(2n)/R \times SO(2k+1) \times SO(2)^{n-k-1}$, $(S)U(n)/(S)(U(2k) \times U(2)^{n-k})$ can be embeded by the method. Particularly, the minimal-dimensional orbits can be described as intersections of quadrics.