A new approach to the eigenvalues of the Gel’fand invariants for the unitary, orthogonal, and symplectic groups

DOI10.1063/1.523535zbMath0366.22014OpenAlexW1965649667MaRDI QIDQ4142015

Stephen A. Edwards

Publication date: 1978

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

Full work available at URL: https://doi.org/10.1063/1.523535

zbMATH Keywords

traceCasimir operatorsGel'fand invariantsWeyl dimension function

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05)

Related Items (15)

General eigenvalue formula for Casimir invariants of type I quantum superalgebras ⋮ Multiplicity-free Wigner coefficients for semisimple Lie groups. I. The U(n) pattern calculus ⋮ Multiplicity-free Wigner coefficients for semisimple Lie groups. II. A pattern calculus for O(n) ⋮ Matrix elements and Wigner coefficients for U q[gl(n)] ⋮ Invariant operators of IU(n) and IO(n) and their eigenvalues ⋮ Unnamed Item ⋮ Second-degree kinematical constraints associated with dynamical symmetries ⋮ Compact relationships between invariants of classical Lie groups and elementary symmetric polynomials ⋮ Casimir invariants and characteristic identities for gl(∞) ⋮ General indices of representations and Casimir invariants ⋮ Generalized projective representations for \(\mathrm{sl}(n+1)\) ⋮ Modified fourth-order Casimir invariants and indices for simple Lie algebras ⋮ New expressions for the eigenvalues of the invariant operators of O(N) and Sp(2n) ⋮ A recursive method for the construction of irreducible representations of the orthogonal group O(n) ⋮ GROUP THEORY FACTORS FOR FEYNMAN DIAGRAMS

Cites Work

• Algebraic identities among U (n) infinitesimal generators
• Eigenvalues of invariants of U(n) and SU(n)
• Eigenvalues of the Casimir operators of the orthogonal and symplectic groups
• A new system of Casimir operators for U(n)
• Canonical Unit Adjoint Tensor Operators in U(n)
• Characteristic Identities for Generators of GL(n), O(n) and Sp(n)

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