Casimir operators, duality, and the point groups

DOI10.1063/1.529671zbMath0801.20022OpenAlexW2044943320MaRDI QIDQ4027869

John J. Sullivan, T. H. Siddall III

Publication date: 9 March 1993

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

Full work available at URL: https://doi.org/10.1063/1.529671

zbMATH Keywords

symmetric groupexpectation valuestwo-body interactionspoint groupclosed expressionsnuclear shell theoryquadratic Casimir operators

Mathematics Subject Classification ID

Nuclear physics (81V35) Applications of Lie groups to the sciences; explicit representations (22E70) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Other geometric groups, including crystallographic groups (20H15) Applications of linear algebraic groups to the sciences (20G45)

Related Items (5)

Some conjectures on \({\mathcal S}_n\)-derived nuclear permutational (or NMR) spin encodings ⋮ Determinable partitional modelling of Cayleyan \(SU(m\leq n/2)\times {\mathcal S}_n\downarrow {\mathcal G}\text{NMR}\) spin symmetries of isotopomeric cage-clusters: Specific \({\mathcal S}_{n\geq 12}\supset \dots\supset {\mathcal D}_3\) group chains, for \({\mathcal S}_n\)-modules in high \(-n\) weak-branching limit. f ⋮ Quaternion-octonion unitary symmetries and analogous Casimir operators ⋮ Indistinguishability in DR \(n\)-fold point-sets \& their \(\mathcal {S}_n\)-invariant dual projective mappings: limitations imposed on Racah-Wigner algebras for Liouville spin dynamics of \([A_{n}X\) multi-invariant NMR systems] ⋮ On \(SU(2)\times{\mathcal S}_{n\geq 12}\) dual-group tensorial sets and carrier spaces in the multiple invariant physics of multiquantum NMR. II: \(\{{\mathcal S}_{12}\supset\cdots\supset [2{\mathcal S}_{2}\}\) pathways from Yamanouchi monomial reductions as \([A]_{12}\) democratic \({\mathcal S}_n\)-invariant labels]

Cites Work

• Recoupling coefficients of the general linear group in bases adapted to shell theories
• Theory of Complex Spectra. IV

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