$k$-Dirac Complexes
Abstract
This is the first paper in a series of two papers. In this paper we construct complexes of invariant differential operators which live on homogeneous spaces of -graded parabolic geometries of some particular type. We call them -Dirac complexes. More explicitly, we will show that each -Dirac complex arises as the direct image of a relative BGG sequence and so this fits into the scheme of the Penrose transform. We will also prove that each -Dirac complex is formally exact, i.e., it induces a long exact sequence of infinite (weighted) jets at any fixed point. In the second part of the series we use this information to show that each -Dirac complex is exact at the level of formal power series at any point and that it descends to a resolution of the -Dirac operator studied in Clifford analysis.
Keywords
Cite
@article{arxiv.1705.09469,
title = {$k$-Dirac Complexes},
author = {Tomas Salac},
journal= {arXiv preprint arXiv:1705.09469},
year = {2018}
}