Eigenvalues of Casimir operators for the general linear, the special linear, and the orthosymplectic Lie superalgebras

DOI10.1063/1.525643zbMath0527.17002OpenAlexW2080878118MaRDI QIDQ3043342

Manfred Scheunert

Publication date: 1983

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

Full work available at URL: https://doi.org/10.1063/1.525643

zbMATH Keywords

highest weight representationsgeneral linear Lie superalgebrasorthosymplectic Lie superalgebraseigenvalues of Casimir elementsepsilon-Lie algebrasgraded tensor calsulusspecial linear Lie superalgebrastwo-index form

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Superalgebras (17A70)

Related Items (12)

The Capelli problem for \(\mathfrak{gl}(m|n)\) and the spectrum of invariant differential operators ⋮ Invariant supersymmetric multilinear forms and the Casimir elements of P-type Lie superalgebras ⋮ On \(\mathfrak{osp}(p+1,q+1|2r)\)-equivariant quantizations ⋮ Invariants and reduced matrix elements associated with the Lie superalgebra gl(m|n) ⋮ Perturbative analysis of the colored Alexander polynomial and KP soliton \(\tau\)-functions ⋮ The first fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ Casimir elements of ε Lie algebras ⋮ Cohomology of Lie superalgebras and their generalizations ⋮ Quantum Berezinian and the classical Capelli identity ⋮ Centre and representations of small quantum superalgebras at roots of unity ⋮ Eigenvalues of Casimir invariants for Uq[osp(m∣n)] ⋮ New expressions for the eigenvalues of the invariant operators of the general linear and the orthosymplectic Lie superalgebras

Cites Work

• A remarkable connection between the representations of the Lie superalgebras osp(1,2n) and the Lie algebras o(2n+1)
• Casimir elements of ε Lie algebras
• Graded tensor calculus
• Generalized Lie algebras
• Casimir invariants and characteristic identities for generators of the general linear, special linear and orthosymplectic graded Lie algebras
• Characters of typical representations of classical lie superalgebras
• CASIMIR OPERATORS FOR SEMISIMPLE LIE GROUPS
• Lie superalgebras

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