Publication at Faculty of Mathematics and Physics |
2015
Abstract
Recently, the Fischer decomposition for polynomials on superspace R^(m|2n) (that is, polynomials in m commuting and 2n anti-commuting variables) has been obtained unless the superdimension M = m - 2n is even and non-positive. In this case, it turns out that the Fischer decomposition of polynomials into spherical harmonics is quite analogous as in R^m and it is an irreducible decomposition under the natural action of Lie superalgebra osp(m|2n).
In this paper, we describe explicitly the Fischer decomposition in the exceptional case. In particular, we show that, under the action of osp(m|2n), the Fischer decomposition is not, in general, a decomposition into irreducible but just indecomposable pieces.