On the Generalized Exchange Operators for SU(n)

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Abstract
By following the work of Biedenharn we have redefined the k‐particles generalized exchange operators (g.e.o.'s) and studied their properties. By a straightforward but cumbersome calculation we have derived the expression, in terms of the SU(n) Casimir operators, of the 2‐, 3‐, or 4‐particle g.e.o. acting on the A‐particle states which span an irreducible representation of the grown SU(n). A striking and interesting result is that the eigenvalues of each of these g.e.o.'s do not depend on the n in SU(n) but only on the Young pattern associated with the irreducible representation considered. For a given g.e.o., the eigenvalues corresponding to two conjugate Young patterns are the same except for the sign which depends on the parity of the g.e.o. considered. Three appendices deal with some related problems and, more specifically, Appendix C contains a method of obtaining the eigenvalues of Gel'fand invariants in a new and simple way.