Abstract
The representation theory of the groupsSO(5),SO(4, 1),SO(6) andSO(5, 1) is studied using the method of Master Analytic Representations (MAR). It is shown that a single analytic expression for the matrix elements of the generators ofSO(n+1) andSO(n, 1) in anSO(n) basis yields all the unitary representations (forn=4,5); and that the compact and non-compact groups have essentially the same analytic representation. Once the MAR of a group is worked out, the search for the unitary irreducible representations is reduced to a purely arithmetic operation. The utmost care has been exercised to conduct the discussions at an elementary level: knowledge of simple angular momentum theory is the only prerequisite.
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Work supported in part by the National Science Foundation.
Work supported in part by the U.S. Atomic Energy Commission.
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Kuriyan, J.G., Mukunda, N. & Sudarshan, E.C.G. Master Analytic Representations and unified representation theory of certain orthogonal and pseudo-orthogonal groups. Commun.Math. Phys. 8, 204–227 (1968). https://doi.org/10.1007/BF01645857
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DOI: https://doi.org/10.1007/BF01645857