General eigenvalue formula for Casimir invariants of type I quantum superalgebras

DOI10.1063/1.531519zbMath0910.17006OpenAlexW1966575456WikidataQ60732540 ScholiaQ60732540MaRDI QIDQ5284285

J. R. Links, Mark D. Gould

Publication date: 27 March 1999

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

Full work available at URL: https://espace.library.uq.edu.au/view/UQ:299749/UQ299749_OA.pdf

zbMATH Keywords

Yang-Baxter equationirreducible representationsClebsch-Gordan coefficientsCasimir invariantsquantum superalgebraseigenvalue formulasupertrace formula

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Superalgebras (17A70)

Related Items (2)

Eigenvalues of Casimir invariants for type I quantum superalgebras ⋮ Quantum matrix algebras of the \(\text{GL}(m|n)\) type: the structure and spectral parameterization of the characteristic subalgebra

Cites Work

• Quantum Berezinian and the classical Capelli identity
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum group invariants and link polynomials
• Universal \(R\)-matrix for quantized (super)algebras
• Universal R-matrices for quantum groups associated to simple Lie superalgebras
• Serre-type relations for special linear Lie superalgebras
• Two variable link polynomials from quantum supergroups
• On the tensor product of a finite and an infinite dimensional representation
• Casimir invariants and infinitesimal characters for semi-simple Lie algebras
• Polynomial identities for simple Lie superalgebras
• Eigenvalues of Casimir operators for the general linear and orthosymplectic Lie superalgebras
• Classification of all star and grade star irreps of gl(n‖1)
• Graded solutions of the Yang-Baxter relation and link polynomials
• Generalized Gel’fand invariants and characteristic identities for quantum groups
• Universal R matrices and invariants of quantum supergroups
• Universal L operator and invariants of the quantum supergroup U q (gl(m/n))
• A new approach to the eigenvalues of the Gel’fand invariants for the unitary, orthogonal, and symplectic groups
• Finite dimensional irreducible representations of the quantum supergroup Uq (gl(m/n))
• Eigenvalues of Casimir invariants of Uq (gl(m/n))
• Unitarity and complete reducibility of certain modules over quantized affine Lie algebras
• Multiparameter link invariants from quantum supergroups
• Two-Dimensional Integrable Models in Quantum Field Theory
• Finite-dimensional representations of U_q(C(n+1)) at arbitrary q
• Classification of finite dimensional unitary irreps for U q[gl(m‖n)]

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