The U n,1 and IUn Representation Matrix Elements

DOI10.1063/1.1665887zbMath0242.22018OpenAlexW1988241731MaRDI QIDQ5652918

Kurt Bernardo Wolf

Publication date: 1972

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

Full work available at URL: https://doi.org/10.1063/1.1665887

Mathematics Subject Classification ID

Applications of Lie groups to the sciences; explicit representations (22E70)

Related Items (8)

Representation matrix elements and Clebsch–Gordan coefficients of the semisimple Lie groups ⋮ Canonical transforms. II. Complex radial transforms ⋮ The algebra and group deformations Im [SO(n)⊗SO(m)⇒SO(n,m), Im [U(n)⊗U(m)]⇒U(n,m), and Im [Sp(n)⊗Sp(m)]⇒Sp(n,m) for 1⩽m⩽n] ⋮ Matrix elements of the generators of I U (n) and I O (n) and respective deformations to U (n,1) and O (n,1) ⋮ Euler angle parametrization of the complex rotation group and its subgroups. I ⋮ Explicit evaluation of the representation functions of IU(n) ⋮ Deformations of inhomogeneous classical Lie algebras to the algebras of the linear groups ⋮ The group chain S On,1⊃S O1,1⊗S On−1, a complete solution to the ``missing label problem

Cites Work

• Discrete degenerate representations of non-compact unitary groups
• A classification of the unitary irreducible representations of \(\mathrm{SU}(N,1)\)
• Irreducible unitary representations of the Lorentz group
• A Set of Harmonic Functions for the Group SU(3)
• Operators that Lower or Raise the Irreducible Vector Spaces of U n−1 Contained in an Irreducible Vector Space of Un
• Representations of finite U3 transformations
• Decomposition of the Unitary Irreducible Representations of the Group SL(2C) Restricted to the Subgroup SU(1, 1)
• Class of Representations of the IU(n) and IO(n) Algebras and Respective Deformations to U(n, 1), O(n, 1)
• Finite Transformations of SU3
• Complete Sets of Functions on Homogeneous Spaces with Compact Stabilizers
• Euler Factorization of SO(p, q) and SU(p, q) Groups
• Matrix Elements for the Most Degenerate Continuous Principal Series of Representations of SO(p, 1)
• On the Contraction of Groups and Their Representations

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