pith. sign in

arxiv: 1508.03426 · v1 · pith:N5XFYZPPnew · submitted 2015-08-14 · 🧮 math.CV · math-ph· math.MP· math.RT

Fischer decomposition for polynomials on superspace

classification 🧮 math.CV math-phmath.MPmath.RT
keywords decompositionfischerpolynomialsactioncaseevenirreduciblenon-positive
0
0 comments X
read the original 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 when M is even and non-positive. In particular, we show that, under the action of osp(m|2n), the Fischer decomposition is not, in general, a decomposition into irreducible but indecomposable pieces.

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.