On representations of the groups Sp(n,1) and Sp(n)

DOI10.1016/0034-4877(85)90025-4zbMath0591.22014OpenAlexW2035997127MaRDI QIDQ1074730

A. U. Klimyk, P. I. Holod

Publication date: 1985

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0034-4877(85)90025-4

zbMATH Keywords

symplectic groupirreducible unitary representationshighest weightsClebsch-Gordan coefficientsinfinitesimal operators

Mathematics Subject Classification ID

Supersymmetric field theories in quantum mechanics (81T60) Nuclear physics (81V35) Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Applications of Lie groups to the sciences; explicit representations (22E70) Unitary representations of locally compact groups (22D10)

Related Items

Degenerate principal series representations of \(\text{Sp}(p,q)\) ⋮ The Jordan–Schwinger representations of Cayley–Klein groups. III. The symplectic groups ⋮ Non-skew-symmetric classical r-matrices and integrable ``\(p_x +ip_y\) proton-neutron BCS models ⋮ Rational r-matrices, higher rank Lie algebras and integrable proton-neutron BCS models ⋮ The analysis of Lagrangian and Hamiltonian properties of the classical relativistic electrodynamics models and their quantization ⋮ The spectral and differential geometric aspects of a generalized De Rham--Hodge theory related with Delsarte transmutation operators in multidimension and its applications to spectral and soliton problems

Cites Work

• Szegoe kernels associated with discrete series
• Intertwining operators for semisimple groups
• Representation matrix elements and Clebsch–Gordan coefficients of the semisimple Lie groups
• Representations of the groups Sp(n,R) and Sp(n) in a U(n) basis
• The most degenerate irreducible representations of the symplectic group
• Composition factors of the principal series representations of the group 𝑆𝑝(𝑛,1)
• On the dynamical symmetries of the Kepler problem
• Some simple R5 Wigner coefficients and their application
• Degenerate Representations of the Symplectic Groups. I. The Compact Group Sp(n)
• Representations of a Semisimple Lie Group on a Banach Space. I
• The Plancherel Formula For Complex Semisimple Lie Groups
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item