Kostant's formula for Kac-Moody Lie algebras

DOI10.1016/0021-8693(92)90010-JzbMath0779.17024WikidataQ115365609 ScholiaQ115365609MaRDI QIDQ1188277

Lishi Liu

Publication date: 13 August 1992

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

zbMATH Keywords

Weyl-Kac character formulaKac-Moody Lie algebrasdominant integral highest weightKostant's cohomology and homology formulasresolution of the irreducible highest weight 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 (25)

Structure and Root Multiplicities for Two Classes of Extended Hyperbolic Kac–Moody Algebras and for all Cases ⋮ Generalized Kac-Moody algebras and some related topics ⋮ The recursive dimension formula for graded lie algebras and its applications ⋮ Extended-Hyperbolic Kac–Moody Algebras Structure and Root Multiplicities ⋮ ON ROOT MULTIPLICITIES OF $H A_n^{(1)}$ ⋮ Root multiplicities of Kac-Moody algebras ⋮ A resolution for standard modules of Borcherds Lie algebras ⋮ Dimension formula for graded Lie algebras and its applications ⋮ Generic free resolutions and root systems ⋮ Irreducible characters of Kac-Moody Lie superalgebras ⋮ Super duality and homology of unitarizable modules of Lie algebras ⋮ Koszul modules of Kac-Moody Lie algebras ⋮ Irreducible characters of general linear superalgebra and super duality ⋮ Rank 2 symmetric hyperbolic Kac-Moody algebras ⋮ Root multiplicities of extended-hyperbolic kac-moody algebras ⋮ Kostant's theorem for a certain class of generalized Kac-Moody algebras ⋮ \(\mathfrak u\)-cohomology formula for unitarizable modules over general linear superalgebras ⋮ Peterson-type dimension formulas for graded Lie superalgebras ⋮ Kostant homology formulas for oscillator modules of Lie superalgebras ⋮ A STUDY ON THE HOMOLOGY MODULES AND THE STRUCTURE OF MAXIMAL IDEAL OF SUPER HYPERBOLIC KAC-MOODY ALGEBRAS SH_{n}^{(3)}, n=96,97,98 ⋮ Root Supermultiplicities of Some Borcherds Superalgebras ⋮ Unnamed Item ⋮ Projective modules over classical Lie algebras of infinite rank in the parabolic category ⋮ Generalized Kac-Moody algebras and the modular function \(j\) ⋮ The strong Bernstein-Gelfand-Gelfand resolution for generalized Kac-Moody algebras. I: The existence of the resolution

Cites Work

• Lie algebra homology and the Macdonald-Kac formulas
• Lie algebra cohomology and the generalized Borel-Weil theorem
• Tits' systems with crystallographic Weyl groups
• Generalized Verma modules, loop space cohomology and MacDonald-type identities
• Une nouvelle démonstration d'un théorème de R. Bott et B. Kostant
• Unnamed Item
• Unnamed Item

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