Projecting on polynomial Dirac spinors. (English) Zbl 1121.15027

Mladenov, Ivaïlo (ed.) et al., Proceedings of the 8th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 9–14, 2006. Sofia: Bulgarian Academy of Sciences (ISBN 978-954-8495-37-0/pbk). 121-126 (2007).
Summary: We adapt S. Axler and W. Ramey’s method [Proc. Am. Math. Soc. 123, No. 12, 3765–3773 (1995; Zbl 0848.31002)] of constructing the harmonic part of a homogeneous polynomial to the Fischer decomposition associated to Dirac operators acting on polynomial spinors. The result yields a constructive solution to a Dirichlet-like problem with polynomial boundary data.
For the entire collection see [Zbl 1108.53003].


15A66 Clifford algebras, spinors
31B05 Harmonic, subharmonic, superharmonic functions in higher dimensions
31B20 Boundary value and inverse problems for harmonic functions in higher dimensions
81R25 Spinor and twistor methods applied to problems in quantum theory


Zbl 0848.31002