Classification of irreducible nonzero level modules with finite-dimensional weight spaces for affine Lie algebras

DOI10.1006/jabr.2000.8648zbMath1017.17008OpenAlexW2080410927WikidataQ115395733 ScholiaQ115395733MaRDI QIDQ5936913

Vyacheslav M. Futorny, A. A. Tsyl'ke

Publication date: 15 June 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2000.8648

zbMATH Keywords

affine algebradense moduleweight module

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (16)

Irreducible \(A_1^{(1)}\)-modules from modules over two-dimensional non-abelian Lie algebra ⋮ New irreducible modules for Heisenberg and affine Lie algebras ⋮ Integrable modules for affine Lie superalgebras ⋮ Classification of level zero irreducible integrable modules for twisted full toroidal Lie algebras ⋮ The category of weight modules for symplectic oscillator Lie algebras ⋮ A Kazhdan-Lusztig correspondence for \(L_{-\frac{3}{2}}(\mathfrak{sl}_3)\) ⋮ New simple \(\widehat{\mathfrak{sl}}_2\)-modules from Weyl algebra modules ⋮ Whittaker modules for the affine Lie algebra \(A_1^{(1)}\) ⋮ Finite weight modules over twisted affine Lie superalgebras ⋮ Structure of parabolically induced modules for affine Kac-Moody algebras ⋮ Modules of highest weight type for the algebra of derivations over a rational quantum torus ⋮ Localization of free field realizations of affine Lie algebras ⋮ Tight irreducible finite weight modules over twisted affine Lie superalgebras ⋮ New representations of affine Kac-Moody algebras ⋮ Representations of Lie algebras ⋮ Classification of Harish-Chandra Modules for Current Algebras

Cites Work

• Unnamed Item
• Irreducible non-dense \(A_ 1^{(1)}\)-modules
• Classification of loop modules with finite dimensional weight spaces
• Classification of irreducible weight modules
• Pointed torsion free modules of affine lie algebras
• Lie Algebra Modules with Finite Dimensional Weight Spaces, I
• On Level 0 Affine Lie Modules
• Simple A₂-modules with a finite dimensional weight space

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