Hyperbolic planes
نویسنده
چکیده
A plane is a two-dimensional right vector space V over a division algebra D, which we assume in this paper has an involution; a hermitian form h : V × V −→ D is hyperbolic, if, with respect to a properly choosen basis, it is given by the matrix 0 1 1 0 ) ; the pair (V, h) is called a hyperbolic plane. If D is central simple over a number field K, a hyperbolic plane (V, h) gives rise to a reductive K-group GD = U(V, h) and a simple K-group SGD = SU(V, h). In this paper we study the case where the real Lie group G(R) is of hermitian type, in other words that the symmetric space of maximal compact subgroups of G(R) is a hermitian symmetric space. Let d = degD (that is, dimKD = d 2); we consider the following cases:
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