Exceptional groups, symmetric spaces and applications
In this article we provide a detailed description of a technique to obtain a simple parameterization for different exceptional Lie groups, such as G{sub 2}, F{sub 4} and E{sub 6}, based on their fibration structure. For the compact case, we construct a realization which is a generalization of the Euler angles for SU(2), while for the non compact version of G{sub 2(2)}/SO(4) we compute the Iwasawa decomposition. This allows us to obtain not only an explicit expression for the Haar measure on the group manifold, but also for the cosets G{sub 2}/SO(4), G{sub 2}/SU(3), F{sub 4}/Spin(9), E{sub 6}/F{sub 4} and G{sub 2(2)}/SO(4) that we used to find the concrete realization of the general element of the group. Moreover, as a by-product, in the simplest case of G{sub 2}/SO(4), we have been able to compute an Einstein metric and the vielbein. The relevance of these results in physics is discussed.
- Research Organization:
- Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (US)
- Sponsoring Organization:
- Physics Division
- DOE Contract Number:
- AC02-05CH11231
- OSTI ID:
- 960437
- Report Number(s):
- LBNL-1938E
- Country of Publication:
- United States
- Language:
- English
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