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A simplified proof of a theorem about group representations
Author(s) -
Reid Charles E.
Publication year - 1972
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.560060216
Subject(s) - simple (philosophy) , representation (politics) , mathematics , group (periodic table) , dimension (graph theory) , order (exchange) , algebraic number , divisor (algebraic geometry) , algebra over a field , representation theory , irreducible representation , representation theorem , pure mathematics , discrete mathematics , physics , mathematical analysis , quantum mechanics , philosophy , epistemology , finance , politics , political science , law , economics
It is a standard theorem of group representation theory that the dimension of an irreducible representation is a divisor of the order of the group. This paper gives a new, relatively simple proof, intended to make the theorem understandable to readers unfamiliar with algebraic integers.