The Bott–Borel–Weil Theorem for direct limit groups

DOI10.1090/S0002-9947-01-02452-7zbMath0994.22013OpenAlexW1532654077MaRDI QIDQ2731958

Joseph A. Wolf, Enriqueta Rodríguez-Carrington, Loki Natarajan

Publication date: 30 July 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02452-7

zbMATH Keywords

direct limitinfinite dimensional Lie groupBorel-Weil theoremBott-Borel-Weil theoremdiagonal embeddingdiagonal Lie algebradirect limit cohomologydirect limit Lie groupdirect limit representationinverse limit cohomologyinverse limit representation

Mathematics Subject Classification ID

Infinite-dimensional holomorphy (46G20) Analysis on real and complex Lie groups (22E30) Applications of Lie groups to the sciences; explicit representations (22E70) Infinite-dimensional Lie groups and their Lie algebras: general properties (22E65) Compact groups (22C05) Complex manifolds (32Q99)

Related Items (9)

Geometric representation theory for unitary groups of operator algebras ⋮ Conical representations for direct limits of symmetric spaces ⋮ Representations of currents taking values in a totally disconnected group ⋮ Towards a Lie theory of locally convex groups ⋮ A construction of generalized Harish-Chandra modules for locally reductive Lie algebras ⋮ Iwasawa decompositions of some infinite-dimensional Lie groups ⋮ Integrability of analytic almost complex structures on Banach manifolds ⋮ Hilbert--Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry ⋮ Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups

Cites Work

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• Partially integrable highest weight modules
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• The Separable Representations of U(H)
• Simple Diagonal Locally Finite Lie Algebras
• Diagonal direct limits of simple lie algebras
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• The sets of the direct limits of lie algebras of the type a
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