TY - CHAP
A1 - Lavicka, Roman
A1 - Delanghe, Richard
A1 - Soucek, Vladimir
ED - Gürlebeck, Klaus
ED - Könke, Carsten
T1 - THE HOWE DUALITY FOR HODGE SYSTEMS
N2 - In this note, we describe quite explicitly the Howe duality for Hodge systems and connect it with the well-known facts of harmonic analysis and Clifford analysis. In Section 2, we recall briefly the Fisher decomposition and the Howe duality for harmonic analysis. In Section 3, the well-known fact that Clifford analysis is a real refinement of harmonic analysis is illustrated by the Fisher decomposition and the Howe duality for the space of spinor-valued polynomials in the Euclidean space under the so-called L-action. On the other hand, for Clifford algebra valued polynomials, we can consider another action, called in Clifford analysis the H-action. In the last section, we recall the Fisher decomposition for the H-action obtained recently. As in Clifford analysis the prominent role plays the Dirac equation in this case the basic set of equations is formed by the Hodge system. Moreover, analysis of Hodge systems can be viewed even as a refinement of Clifford analysis. In this note, we describe the Howe duality for the H-action. In particular, in Proposition 1, we recognize the Howe dual partner of the orthogonal group O(m) in this case as the Lie superalgebra sl(2 1). Furthermore, Theorem 2 gives the corresponding multiplicity free decomposition with an explicit description of irreducible pieces.
KW - Angewandte Informatik
KW - Angewandte Mathematik
KW - Architektur
KW - Computerunterstütztes Verfahren
KW - Computer Science Models in Engineering; Multiscale and Multiphysical Models; Scientific Computing
Y1 - 2010
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170314-28669
UR - http://euklid.bauing.uni-weimar.de/ikm2009/paper.html
SN - 1611-4086
ER -