Representations of 𝒢+++ and the role of space-time View Full Text


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Article Info

DATE

2004-02-12

AUTHORS

Axel Kleinschmidt, Peter West

ABSTRACT

We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras +++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of +++. In particular, for E8+++, this applies to all its fundamental representations. However, there are some important examples, such as AN−3+++, where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on +++. Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of +++ which is consistent with the interpretation of the former as charges associated with brane solutions. More... »

PAGES

033

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1088/1126-6708/2004/02/033

DOI

http://dx.doi.org/10.1088/1126-6708/2004/02/033

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1011603707


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