On the existence of \(({\mathfrak g},{\mathfrak k})\)-modules of finite type

DOI10.1215/S0012-7094-04-12525-4zbMath1097.17007MaRDI QIDQ1766226

Gregg J. Zuckerman, Vera V. Serganova, I. B. Penkov

Publication date: 28 February 2005

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.dmj/1098892272

zbMATH Keywords

D-modules(g,k)-modulesFernando-Kac subalgebrasprimal subalgebrasroot subalgebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Semisimple Lie groups and their representations (22E46)

Related Items (11)

Supports of \((\mathfrak g,\mathfrak k)\)-modules of finite type ⋮ Dirac cohomology and orthogonality relations for weight modules ⋮ Bounded reductive subalgebras of \(\mathfrak{sl}_n\) ⋮ Categories of bounded \((\mathfrak{sp}(\mathrm{S}^2V\oplus\mathrm{S}^2V^\ast)\), \(\mathfrak{gl}(V))\)- and \((\mathfrak{sp}(\Lambda ^2 V\oplus\Lambda ^2V^\ast)\), \(\mathfrak{gl}(V))\)-modules ⋮ On bounded generalized Harish-Chandra modules ⋮ On the structure of simple bounded weight modules of sl(∞),o(∞),sp(∞) ⋮ Eigenvalue coincidences and \(K\)-orbits. I ⋮ Root Fernando-Kac subalgebras of finite type ⋮ Unnamed Item ⋮ On categories of admissible \(( \mathfrak{g}, \mathrm{sl}(2))\)-modules ⋮ A construction of generalized Harish-Chandra modules for locally reductive Lie algebras

Cites Work

• On irreducible \(A_ 2\)-finite \(G_ 2\)-modules
• Representations of real reductive Lie groups
• Classification of irreducible weight modules
• Lie Algebra Modules with Finite Dimensional Weight Spaces, I
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