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24 April 2024
 
  » arxiv » 1602.4116

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Higher spin representations of K(E10)
Axel Kleinschmidt ; Hermann Nicolai ;
Date 12 Feb 2016
AbstractWe review the recently constructed non-trivial fermionic representations of the infinite-dimensional subalgebra K(E10) of the hyperbolic Kac--Moody algebra E10. These representations are all unfaithful (and more specifically, of finite dimension). In addition we present their decompositions under the various finite-dimensional subgroups associated with some maximal supergravities in dimensions D<=11, and the projectors for ’spin-7/2’ which have not been given before. Those representations that have not been derived from supergravity still have to find a role and a proper physical interpretation in the conjectured correspondence between E10 and M-theory. Nevertheless, they provide novel mathematical structures that could shed some light on fundamental questions in supergravity and on the possible role of K(E10) as an ’R-symmetry’ of M-theory, and perhaps also on the algebra E10 itself.
Source arXiv, 1602.4116
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