An Explicit Basis for the Reduction U(n + m) ↓ U(n) × U(m)

DOI10.1063/1.1665546zbMath0231.22021OpenAlexW2103397515MaRDI QIDQ5638508

Jouko Mickelsson

Publication date: 1971

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

Full work available at URL: https://doi.org/10.1063/1.1665546

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70) Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) (22E47)

Related Items (8)

Reduction of inner-product representations of unitary groups ⋮ Current algebra representation for the \(3+1\) dimensional Dirac-Yang-Mills theory ⋮ Branching rules for unitary groups and spectra of invariant differential operators on complex Grassmannians ⋮ Lowering operators and the symplectic group ⋮ Lowering operators for the reduction U(\(n\)) \(\downarrow\) SO (\(n\)) ⋮ Step algebras of semi-simple subalgebras of Lie algebras ⋮ Determination of basis for the irreducible representations of the unitary group for U( p+q)↓U( p)⊗U( q) ⋮ The group chain S On,1⊃S O1,1⊗S On−1, a complete solution to the ``missing label problem

Cites Work

• Operators that Lower or Raise the Irreducible Vector Spaces of U n−1 Contained in an Irreducible Vector Space of Un
• Bases for the Irreducible Representations of the Unitary Groups and Some Applications
• Bases for Irreducible Representations of U2n in the Chain U2n⊃Un+̇Un

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