Pure Mathematics
en
Representations of 𝒢+++ and the role of space-time
2004-02-12
2019-04-10T18:50
articles
https://scigraph.springernature.com/explorer/license/
research_article
http://iopscience.iop.org/article/10.1088/1126-6708/2004/02/033/meta
033
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.
true
2004-02-12
02
10.1088/1126-6708/2004/02/033
doi
University of Cambridge
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, U.K.
1029-8479
Journal of High Energy Physics
1126-6708
Kleinschmidt
Axel
2004
Mathematical Sciences
West
Peter
readcube_id
37492f251a6c50feb0370b4bdfadd1f0cd3724c17866a2017beb2423f12e7e4d
pub.1011603707
dimensions_id
King's College London
Department of Mathematics, King's College, London WC2R 2LS, U.K.
Springer Nature - SN SciGraph project