Unitary highest weight modules

DOI10.1016/0001-8708(87)90049-1zbMath0623.22014OpenAlexW2031182206MaRDI QIDQ1091488

Jeffrey D. Adams

Publication date: 1987

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0001-8708(87)90049-1

zbMATH Keywords

coadjoint orbitssemisimple Lie groupparabolic subalgebraunitary dualderived functor moduleirreducible unitary representationcomplexified Lie algebrasunitary highest weight modulesunitary holomorphic representation

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Semisimple Lie groups and their representations (22E46) Lie algebras of Lie groups (22E60) Unitary representations of locally compact groups (22D10) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

Dirac inequality for highest weight Harish-Chandra modules I, Discrete decomposability of restriction of \(A_{\mathfrak q}(\lambda)\) with respect to reductive subgroups and its applications, Coadjoint orbits and reductive dual pairs, BRANCHING RULES OF SINGULAR UNITARY REPRESENTATIONS WITH RESPECT TO SYMMETRIC PAIRS (A_2n-1, D_n), An \(L^ 2\)-cohomology construction of negative spin mass zero equations for U(p,q), Discrete series representations for the orbit spaces arising from two involutions of real reductive Lie groups, Unnamed Item, Transfer of highest weight modules and small unipotent representations, Dirac inequality for highest weight Harish-Chandra modules II, Unnamed Item, Unnamed Item, SUR LES PAQUETS D’ARTHUR DE CONTENANT DES MODULES UNITAIRES DE PLUS HAUT POIDS, SCALAIRES, Geometric Construction of Certain Highest Weight Modules, Lie algebra cohomology and the resolution of certain Harish-Chandra modules, Hilbert series, Howe duality, and branching rules, Relating signed and classical Kazhdan-Lusztig polynomials, A program for branching problems in the representation theory of real reductive groups, Representations of the Infinite Unitary Group from Constrained Quantization, One-dimensional representations of \({U(p,q)}\) and the Howe correspondence

Cites Work

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• Discrete spectrum of the reductive dual pair \((\mathrm{O}(p,q),\mathrm{Sp}(2m))\)
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