Abstract
Recently, the Fischer decomposition for polynomials on superspace ℝm|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 ℝm 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 ∈ − 2ℕ0. 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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
