n-fold tensor products of GL(N,\({\mathbb{C}})\) and decomposition of Fock spaces

DOI10.1016/0022-1236(89)90109-2zbMath0682.22016OpenAlexW2074448199MaRDI QIDQ1824047

Tuong Ton-That, William H. Klink

Publication date: 1989

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(89)90109-2

zbMATH Keywords

multiplicitytensor productsirreducible representationsFock spacesCasimir operatorsFrobenius reciprocity theoremreduction of representationsfinite-dimensional polynomial spacesorthogonal direct sums

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Complex Lie groups, group actions on complex spaces (32M05) Applications of linear algebraic groups to the sciences (20G45) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items

Algorithms for computing \(U(N)\) Clebsch-Gordan coefficients ⋮ Calculation of Clebsch-Gordan and Recah coefficients using symbolic manipulation programs ⋮ Invariant theory of the block diagonal subgroups of \(GL(n,\mathbb{C})\) and generalized Casimir operators ⋮ Algorithms for computing generalized \(\text{U}(N)\) Racah coefficients

Cites Work

• On a resolution of the multiplicity problem for U(n)
• On the Representations of the Rotation Group
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