Open AccessThe representation ring of a compact Lie group revisited
Author(s) -
Robert Oliver
Publication year - 1998
Publication title -
commentarii mathematici helvetici
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.603
H-Index - 46
eISSN - 1420-8946
pISSN - 0010-2571
DOI - 10.1007/s000140050059
Subject(s) - mathematics , homomorphism , pure mathematics , character (mathematics) , class (philosophy) , lie group , representation of a lie group , adjoint representation , representation (politics) , simple lie group , compact group , ring (chemistry) , group (periodic table) , representation theory , fundamental representation , algebra over a field , discrete mathematics , lie algebra , computer science , artificial intelligence , chemistry , geometry , organic chemistry , politics , political science , law , weight
We describe a new construction of the induction homomorphism for representation rings of compact Lie groups: a homomorphism first defined by Graeme Segal. The idea is to first define the induction homomorphism for class functions, and then show that this map sends characters to characters. This requires a detection theorem - a class function of G is a character if its restrictions to certain subgroups of G are characters - which in turn requires a review of the representation theory for nonconnected compact Lie groups.
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