Orthogonal basis for spherical monogenics by step two branching
Complex Variables
2010-10-11 v1
Abstract
Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R^m. They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on R^m. Fix the direct sum R^m = R^p x R^q. In this paper we will study the decomposition of the space M_n(R^m;C_m) of spherical monogenics of order n under the action of Spin(p) x Spin(q). As a result we obtain a Spin(p) x Spin(q)-invariant orthonormal basis for M_n(R^m;C_m). In particular, using the construction with p = 2 inductively, this yields a new orthonormal basis for the space M_n(R^m;C_m).
Cite
@article{arxiv.1010.1620,
title = {Orthogonal basis for spherical monogenics by step two branching},
author = {R. Lavicka and V. Soucek and P. Van Lancker},
journal= {arXiv preprint arXiv:1010.1620},
year = {2010}
}
Comments
submitted