Algèbre de Jordan et ensemble de Wallach. (Jordan algebra and Wallach set)

DOI10.1007/BF01389085zbMath0622.22008MaRDI QIDQ1090778

Michel Lassalle

Publication date: 1987

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143487

zbMATH Keywords

invariant measuresconvex coneWallach setstructure groupformally real Jordan algebraanalytic continuation of discrete seriesunitarization problemunitary representation of Lie group

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Unitary representations of locally compact groups (22D10) Structure theory for Jordan algebras (17C10) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

When is a Riesz distribution a complex measure?, Maximum boundary regularity of bounded Hua-harmonic functions on tube domains, Why Jordan algebras are natural in statistics: quadratic regression implies Wishart distributions, Characterization of the Jørgensen set in generalized linear models, The Wishart distribution on symmetric cones, Extreme points of the Vandermonde determinant and Wishart ensemble on symmetric cones, Toeplitz C ∗-Algebras on Boundary Orbits of Symmetric Domains, Singular Riesz measures on symmetric cones, Complete monotonicity for inverse powers of some combinatorially defined polynomials, An expectation formula for the multivariate Dirichlet distribution, Branching laws for discrete Wallach points, Eigenvalues of \(K\)-invariant Toeplitz operators on bounded symmetric domains

Cites Work

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• The functional equation of zeta distributions associated with formally real Jordan algebras
• Structure of prehomogeneous spaces associated with certain graded Lie algebras
• A formula in simple Jordan algebras
• Analytic continuation of the holomorphic discrete series of a semi-simple Lie group
• Jordan Algebras and Harmonic Analysis on Symmetric Spaces
• The Analytic Continuation of the Discrete Series. II
• On a Class of Linear Differential Equations for Automorphic Forms in Several Complex Variables