Permutationally invariant 3-dimensional vector spaces of \(3\times 3\) symmetric matrices: a groupoid

DOI10.1007/s11005-023-01664-0zbMath1530.15023OpenAlexW4389792294MaRDI QIDQ6187141

Daniel B. Dix

Publication date: 10 January 2024

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

Full work available at URL: https://doi.org/10.1007/s11005-023-01664-0

zbMATH Keywords

symmetrygroup representationGrassmannianisotropygroupoidpermutation groupsymmetric matrixdiscriminantadiabatic approximationorthogonal matrixtetrahedral groupconical intersectiontriple intersectioneigenvalue intersection

Mathematics Subject Classification ID

Eigenvalues, singular values, and eigenvectors (15A18) Molecular physics (81V55) Linear spaces of operators (47L05) Exterior algebra, Grassmann algebras (15A75) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05) General theory for finite permutation groups (20B05) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40) Orthogonal matrices (15B10)

Cites Work

• Singularities and groups in bifurcation theory. Volume II
• Remarks on eigenvalues and eigenvectors of Hermitian matrices, Berry phase, adiabatic connections and quantum Hall effect
• Discriminant of symmetric matrices as a sum of squares and the orthogonal group
• On the conicity of eigenvalues intersections for parameter-dependent self-adjoint operators
• Molecular propagation through electron energy level crossings
• Beyond Born–Oppenheimer
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