Highest weight representations for gl(m/n) and gl(m+n)

DOI10.1063/1.528323zbMath0682.17013OpenAlexW2065322724MaRDI QIDQ4731347

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Publication date: 1989

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.528323

zbMATH Keywords

representationsladder representationsvector coherent stateatypical representationsReducibilityLie superalgebra \({\mathfrak gl}(m/n)\)Lie algebra \({\mathfrak gl}(m+n)\)Lie superalgebras \({\mathfrak gl}(1/n)\)

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Graded Lie (super)algebras (17B70)

Related Items (8)

Matrix representations of SOn+2 in an SOn×SO2 basis and some isoscalar factors for SOn+2⊇SOn×SO2 ⋮ On the composition factors of Kac modules for the Lie superalgebras sl(m/n) ⋮ Superfield and matrix realizations of highest weight representations for osp(m/2n) ⋮ Transformations of some induced osp(3/2) modules in an so(3)⊕sp(2) basis ⋮ Finite-dimensional representations of the Lie superalgebra gl(2/2) in a gl(2)⊕gl(2) basis. II. Nontypical representations ⋮ Bott–Borel–Weil construction for quantum supergroup Uq(gl(m|n)) ⋮ Character formulas for irreducible modules of the Lie superalgebras sl(m/n) ⋮ Representations of quantum superalgebra U q[gl(2|1) in a coherent state basis and generalization]

Cites Work

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• Vector coherent state representation theory
• Vector coherent state theory and its application to the orthogonal groups
• The matrix representations of g2. I. Representations in an so(4) basis
• New perspective on the U(n) Wigner-Racah calculus. I. Vector coherent state theory and construction of Gel'fand bases
• New perspective on the U(n) Wigner-Racah calculus. II. Elementary reduced Wigner coefficients for U(n)
• Graded Lie algebras: Generalization of Hermitian representations
• Irreducible representations of the osp(2,1) and spl(2,1) graded Lie algebras
• On the Representations of the Semisimple Lie Groups. II
• Canonical Definition of Wigner Coefficients in Un

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