Open AccessPHYSICAL METHOD OF GROUP REPRESENTATION THEORY (Ⅱ)——THE QUASI-STANDARD BASES OF PERMUTATION GROUP AND THE GELFAND BASES OF UNITARY GROUP
Author(s) -
Chen Jin-Chuan,
Fan Wang,
Ming Gao
Publication year - 1977
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.26.427
Subject(s) - group (periodic table) , unitary group , permutation group , permutation (music) , mathematics , symmetric group , unitary state , base (topology) , operator (biology) , eigenfunction , combinatorics , irreducible representation , pure mathematics , algebra over a field , physics , quantum mechanics , mathematical analysis , eigenvalues and eigenvectors , law , biochemistry , chemistry , repressor , political science , acoustics , transcription factor , gene
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.