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PHYSICAL METHOD OF GROUP REPRESENTATION THEORY (Ⅱ)——THE QUASI-STANDARD BASES OF PERMUTATION GROUP AND THE GELFAND BASES OF UNITARY GROUP
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1977
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Coxeter GroupGroup SunQuantum GroupsRepresentation TheoryLinear GroupsGroup GfGroup RepesentationEducationAlgebraic CombinatoricsGroup RepresentationUniversal AlgebraNilpotent GroupGroup Structure
This paper analyses the contradictions which would appear when one applies the traditional theory of group repesentation to gf-the permutation group on state indicies. It is pointed out that when repeated state indicies occur, the permutation operator of gf will become undefined. According to [1], we generalise naturally the concepts of the irreducible bases for such case and give a unambiguous definition of the so called quasi-standard bases of group gf. Futhermore we have proved that the quasi-standard bases of group gf are just the Gelfand bases of group SUn. Hence the eigenfunction methodcan also be used to calculate the Gelfand bases of group SUn.