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Diagram approach to group algebraic methods
Author(s) -
Black R. J.,
Stedman G. E.
Publication year - 1982
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560210507
Subject(s) - duality (order theory) , group (periodic table) , mathematics , invariant (physics) , class (philosophy) , irreducible representation , group theory , diagrammatic reasoning , algebra over a field , representation theory , algebraic number , pure mathematics , group representation , element (criminal law) , combinatorics , computer science , physics , mathematical physics , quantum mechanics , artificial intelligence , mathematical analysis , political science , law , programming language
Class sum theory, the duality with IRREP methods and tensor operators in the group algebra are discussed by generalizing the diagrammatic approach of conventional IRREP theory to include group label manipulation. Concepts such as invariant nodes and Jucys–Levinson–Vanagas reduction theorems generalize straightforwardly. The results are capable of unique simplification for certain nodes, when the group rearrangement theorem is useable or when a class sum is performed. A duality transformation (between IRREP –partner and class–element labels) emerges as an important concept.