Holomorphic highest weight representations of infinite dimensional complex classical groups

DOI10.1515/crll.1998.038zbMath0894.22007OpenAlexW1992935710MaRDI QIDQ4380459

Karl-Hermann Neeb

Publication date: 12 August 1998

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crll.1998.038

zbMATH Keywords

Lie algebraclassical Lie groupunitary highest weight representationholomorphic representationcomplex classical group

Mathematics Subject Classification ID

General properties and structure of complex Lie groups (22E10) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

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Reflection systems and partial root systems ⋮ Schur-Weyl Theory for C *-algebras ⋮ On differentiable vectors for representations of infinite dimensional Lie groups ⋮ Lie-Poisson theory for direct limit Lie algebras ⋮ On the First Order Cohomology of Infinite-Dimensional Unitary Groups ⋮ Semibounded unitary representations of double extensions of Hilbert-loop groups ⋮ A complex semigroup approach to group algebras of infinite dimensional Lie groups ⋮ Towards a Lie theory of locally convex groups ⋮ Unitary highest weight representations in Hilbert spaces of holomorphic functions on infinite dimensional domains ⋮ The structure of locally finite split Lie algebras ⋮ On restricted diagonalization ⋮ Iwasawa decompositions of some infinite-dimensional Lie groups ⋮ Hilbert--Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry ⋮ Tensor Representations of Mackey Lie Algebras and Their Dense Subalgebras ⋮ Central extensions of infinite-dimensional Lie groups ⋮ Representations in \(L^{2}\)-spaces on infinite-dimensional symmetric cones

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