Fischer decomposition for spinor valued polynomials in several variables

Abstract

It is well-known that polynomials decompose into spherical harmonics. This result is called separation of variables or the Fischer decomposition. In the paper we prove the Fischer decomposition for spinor valued polynomials in $k$ vector variables of ${\mathbb{R}}^m$ under the stable range condition $m\ge 2k$. Here the role of spherical harmonics is played by monogenic polynomials, that is, polynomial solutions of the Dirac equation in $k$ vector variables.

References in corpus (2)

• The orthosymplectic superalgebra in harmonic analysis
• Reciprocity Algebras and Branching for Classical Symmetric Pairs

Cited by in corpus (1)

• Bases for infinite dimensional simple $\mathfrak{osp}(1|2n)$-modules respecting the branching $\mathfrak{osp}(1|2n)\supset \mathfrak{gl}(n)$