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Journal of Lie Theory 21 (2011), No. 2, 417--426
Copyright Heldermann Verlag 2011

Real forms of dual pairs g2×h in g of type E6, E7 and E8

Domagoj Kovacevic
Faculty of Electrical Engineering and Computing, University of Zagreb, 10000 Zagreb, Croatia


\def\a{{\frak a}} \def\g{{\frak g}} \def\h{{\frak h}} Let $\g$ be a complex Lie algebra of type $E_6$, $E_7$ or $E_8$ and let $\g_2\times\h$ be a dual pair in $\g$. In this paper, we look for possible real forms of $\g_2\times\h$. It turns out that for each $n$ and for all real forms, say $\a_0\times\h_0$ of $\g_2\times\h$, there exists a real form $\g_0$ of $\g$ such that $\a_0\times\h_0$ embedds into $\g_0$. The full description is given in Theorem 3.1.

Keywords: Dual pairs, real forms.

MSC: 17B05

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