Algebraic structures of Makarevič spaces. I
A Makarevič space is a reductive symmetric space \(X=G/H\) which can be realized as an open symmetric orbit in the conformal compactification of a semisimple Jordan algebra. Recently Makarevič spaces with a causal structure have attracted interest because of the Hardy spaces of holomorphic functions one can construct on certain closely related open domains \(\Xi\) in the complex conformal compactification. In the present paper the author studies the Jordan algebraic description of \(X\) and \(\Xi\). A particular role is played by the Bergman operator, which is an operator valued polynomial generalizing the canonical factor of automorphy associated to a Hermitian symmetric domain, and which yields simple and useful descriptions of \(X\) and \(\Xi\) as well as the invariant measure on \(X\).
scientific article; zbMATH DE number 1139664
scientific article