THE SIGNATURES OF FINITE-DIMENSIONAL REPRESENTATIONS OF THE DE-SITTERGROUPS SO(4,1) AND SO(3,2)

Authors
GRIMM S DEMONTIGNY M PATERA J
Citation
S. Grimm et al., THE SIGNATURES OF FINITE-DIMENSIONAL REPRESENTATIONS OF THE DE-SITTERGROUPS SO(4,1) AND SO(3,2), Journal of physics. A, mathematical and general, 30(21), 1997, pp. 7463-7471
Citations number
27
Categorie Soggetti
Physics,"Physycs, Mathematical
Journal title
Journal of physics. A, mathematical and general → ACNP
ISSN journal
03054470
Volume
30
Issue
21
Year of publication
1997
Pages
7463 - 7471
Database
ISI
SICI code
0305-4470(1997)30:21<7463:TSOFRO>2.0.ZU;2-A
Abstract
The signature of a finite-dimensional orthogonal representation of a s imple Lie group is the difference between the number of positive and n egative signs in the diagonal form of its symmetric bilinear invariant . We derive the expressions for the signatures of all finite-dimension al representations of the de Sitter groups SO(4, 1) and SO(3, 2) in tw o ways. One by means of character values of appropriate elements of ad joint order two on the representation and the other through generating functions.