Exceptional reductions

Starting from basic identities of the group E sub(8), we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E sub(7) x SU (2) and then of E sub(6) x U (1). This procedure provides a systematic approach to the basic identities involving invar...

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Bibliographic Details
Published in:Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2011-04, Vol.44 (15), p.155207-24
Main Authors: Marrani, Alessio, Orazi, Emanuele, Riccioni, Fabio
Format: Article
Language:English
Subjects:
Charge
Exact sciences and technology
Group theory
Invariants
Mathematical analysis
Mathematical models
Physics
Reduction
Supergravity
Tensors
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Summary:Starting from basic identities of the group E sub(8), we perform progressive reductions, namely decompositions with respect to the maximal and symmetric embeddings of E sub(7) x SU (2) and then of E sub(6) x U (1). This procedure provides a systematic approach to the basic identities involving invariant primitive tensor structures of various irreps of finite-dimensional exceptional Lie groups. We derive novel identities for E sub(7) and E sub(6), highlighting the E sub(8) origin of some well-known ones. In order to elucidate the connections of this formalism to four-dimensional Maxwell-Einstein supergravity theories based on symmetric scalar manifolds (and related to irreducible Euclidean Jordan algebras, the unique exception being the triality-symmetric N = 2 stu model), we then derive a fundamental identity involving the unique rank-4 symmetric invariant tensor of the 0-brane charge symplectic irrep of U-duality groups, with potential applications in the quantization of the charge orbits of supergravity theories, as well as in the study of multi-center black hole solutions therein.
ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/44/15/155207