arXiv:hep-th/0503106·v2·High Energy Physics — Theory
Euler angles for G2
Sergio L. Cacciatori🇮🇹 · Bianca L. Cerchiai🇺🇸 · Alberto Della Vedova🇮🇹 · Giovanni Ortenzi🇮🇹 · Antonio Scotti🇮🇹
Abstract
We provide a simple parametrization for the group G2, which is analogous to the Euler parametrization for SU(2). We show how to obtain the general element of the group in a form emphasizing the structure of the fibration of G2 with fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions. In particular this allows us to obtain a simple expression for the Haar measure on G2. Moreover, as a by-product it yields a concrete realization and an Einstein metric for H.
Comments: 21 pages, 2 figures, some misprints corrected