Spinorspaces in discrete Clifford analysis
Representation Theory
2017-01-27 v1
Abstract
In this paper we work in the `split' discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions, defined on the grid Z^m, of the discrete Dirac operator D, involving both forward and backward differences, which factorizes the (discrete) Star-Laplacian (Delta = D^2). We show how the space M_k of discrete homogeneous spherical monogenics of degree k, is decomposable into 2^{2m-n} isomorphic irreducible representations with highest weight (k + 1/2, 1/2,...,1/2) in the odd-dimensional case and two times 2^{2m-n} isomorphic irreducible representations with highest weight (k)'_+ = (k + 1/2, 1/2,...,1/2,1/2) resp. (k)'_- = (k + 1/2, 1/2,...,1/2,-1/2) in the even dimensional case.
Cite
@article{arxiv.1701.07741,
title = {Spinorspaces in discrete Clifford analysis},
author = {Hilde De Ridder and Tim Raeymaekers},
journal= {arXiv preprint arXiv:1701.07741},
year = {2017}
}