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Reduction of Representations of SUm+n with respect to the Subgroup SUm ⊗ SUn
1.C. R. Hagen and A. J. Macfarlane, J. Math. Phys. 6, 1355 (1965), previous paper. This paper is referred to as HM in the present work.
2.An extensive list of references to the theory may be found in HM.
3.F. Gürsey and L. A. Radicati, Phys. Rev. Letters 13, 173 (1964).
4.A. Pais, Phys. Rev. Letters 13, 175 (1964).
5.B. Sakita, Phys. Rev. Letters 13, 418 (1964);
5.and B. Sakita, Phys. Rev. 136, B1756 (1964).
6.F. Gürsey, A. Pais, and L. A. Radicati, Phys. Rev. Letters 13, 299 (1964).
7.M. Gell‐Mann, Physics 1, 63 (1964).
7.M. Moskinsky, J. Math. Phys. 4, 1128 (1963);
7.and T. A. Brody, M. Moshinsky, and I. Renero, ibid (to be published).
8.E. P. Wigner, Phys. Rev. 51, 106 (1937);
8.E. P. Wigner and E. Feenberg, Rept. Progr. Phys. 8, 274 (1941).
9.Connection with the highest weight notation is explained in C. R. Hagen and A. J. Macfarlane, J. Math. Phys. 5, 1335 (1964), footnote 11.
10.D. E. Littlewood, Theory of Group Characters (Oxford University Press, London, 1950), 2nd ed., especially Chaps. 5 and 6.
11.Such series can be obtained for any unitary group by the Young diagram method; see D. E. Littlewood, Ref. 10, p. 94.
12.D. E. Littlewood, Ref. 10, p. 104.
13.D. E. Littlewood, Ref. 10, p. 105.
14.M. Whippman in a recent investigation of branching rules (preprint, 1964) has also given the result and indicated that it can be made the basis of a recursive derivation of results such as those derived in the present work. See also A. J. Coleman, unpublished notes of lectures given at University of Uppsala, Uppsala, Sweden, 1963.
15.A further partial check of results can be attained as follows. From the reduction of IRs (see Table I of HM) and the known Y content of IRs, we may obtain the multiplicity of each Y value in any given IR of This can be compared with what follows from Table I of the present work and use of known dimensionalities for and IRs.
16.C. R. Hagen and A. J. Macfarlane, J. Math. Phys. 5, 1335 (1964).
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