TY  - CONF
A1  - Soucek, Vladimir
A2  - Gürlebeck, Klaus
A2  - Könke, Carsten
T1  - ON MASSLESS FIELD EQUATION IN HIGHER DIMENSIONS
N2  - The paper is devoted to a study of properties of homogeneous solutions of massless field equation in higher dimensions. We first treat the case of dimension 4. Here we use the two-component spinor language (developed for purposes of general relativity). We describe how are massless field operators related to a higher spin analogues of the de Rham sequence - the so called Bernstein-Gel'fand-Gel'fand (BGG) complexes - and how are they related to the twisted Dirac operators. Then we study similar question in higher (even) dimensions. Here we have to use more tools from representation theory of the orthogonal group. We recall the definition of massless field equations in higher dimensions and relations to higher dimensional conformal BGG complexes. Then we discuss properties of homogeneous solutions of massless field equation. Using some recent techniques for decomposition of tensor products of irreducible $Spin(m)$-modules, we are able to add some new results on a structure of the spaces of homogenous solutions of massless field equations. In particular, we show that the kernel of the massless field equation in a given homogeneity contains at least on specific irreducible submodule.
KW  - Angewandte Informatik
KW  - Angewandte Mathematik
KW  - Architektur <Informatik>
KW  - Computerunterstütztes Verfahren
KW  - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1  - 2010
UR  - https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/2892
UR  - https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20170314-28925
UR  - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN  - 1611-4086
ER  -