Publication at Faculty of Mathematics and Physics |
2009
Abstract
Rarita-Schwinger operators (or Higher Spin Dirac operators) are generalizations of the Dirac operator to functions valued in representations S_k with higher spin k. Their algebraic and analytic properties are currently studied in Clifford analysis.
As a part of this pursuit, we describe the algebra of invariant End S_k-valued polynomials, i.e. the algebra of invariant constant-coefficient differential operators acting on these representations. The main theorem states that this algebra is generated by the powers of the Rarita-Schwinger and Laplace operators.
This algebra is the algebraic part of the Howe dual superalgebra corresponding to the Pin group acting on S_k.