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  K(E9) from K(E10)

Kleinschmidt, A., Nicolai, H., & Palmkvist, J. (2007). K(E9) from K(E10). Journal of High Energy Physics, 2007(6): 051. doi:10.1088/1126-6708/2007/06/051.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-48DC-0 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-48DE-C
Genre: Journal Article

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 Creators:
Kleinschmidt, Axel1, Author
Nicolai, Hermann1, Author              
Palmkvist, Jakob1, Author              
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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 Abstract: We analyse the M-theoretic generalisation of the tangent space structure group after reduction of the D=11 supergravity theory to two space-time dimensions in the context of hidden Kac-Moody symmetries. The action of the resulting infinite-dimensional `R symmetry' group K(E9) on certain unfaithful, finite-dimensional spinor representations inherited from K(E10) is studied. We explain in detail how these representations are related to certain finite codimension ideals within K(E9), which we exhibit explicitly, and how the known, as well as new finite-dimensional `generalised holonomy groups' arise as quotients of K(E9) by these ideals. In terms of the loop algebra realisations of E9 and K(E9) on the fields of maximal supergravity in two space-time dimensions, these quotients are shown to correspond to (generalised) evaluation maps, in agreement with previous results of Nicolai and Samtleben (hep-th/0407055). The outstanding question is now whether the related unfaithful representations of K(E10) can be understood in a similar way.

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 Dates: 2007
 Publication Status: Published in print
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 Identifiers: eDoc: 293637
URI: http://www.iop.org/EJ/abstract/1126-6708/2007/06/051
Other: arXiv:hep-th/0611314
DOI: 10.1088/1126-6708/2007/06/051
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Title: Journal of High Energy Physics
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Pages: - Volume / Issue: 2007 (6) Sequence Number: 051 Start / End Page: - Identifier: ISSN: 1126-6708