Algèbre de Jordan et ensemble de Wallach. (Jordan algebra and Wallach set)
The main theme of this paper is to formulate the problem of determining the relatively invariant measures on a closure of a convex cone in a formally real Jordan algebra and to solve it. Let A be a formally real Jordan algebra whose unit is E. Let \({\mathbb{G}}\) be the connected component of the structure group of A containing the neutral element and let \(\Omega\) be the \({\mathbb{G}}\)-orbit of \(e\in A\). Then the closure \({\bar \Omega}\) decomposes into a finite number of \({\mathbb{G}}\)-orbits. The author proves that each orbit in \(\Omega\) has relatively invariant measures and determines all of them. This contributes to the determination of the Wallach set, which is defined in relation to the unitarization problem of analytic continuation of discrete series.
analytic continuation of discrete series
scientific article; zbMATH DE number 4008701