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Irreducible Root Systems and Finite Linear Groups of Degree Two
Author(s) -
Drucker Daniel,
Frohardt Daniel
Publication year - 1982
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/14.2.142
Subject(s) - mathematics , root (linguistics) , character (mathematics) , pure mathematics , degree (music) , connection (principal bundle) , group of lie type , combinatorics , group theory , geometry , philosophy , linguistics , physics , acoustics
Several authors have noted an interesting connection between the finite subgroups of SL(2, C) and the irreducible root systems having a single root length. Recently McKay discovered that eigenmatrices of the extended Cartan matrices of types A , D , and E can be described as character tables of the finite nontrivial subgroups of SL(2, C). By considering pairs of these groups, where one group is embedded in the other, we generalize McKay's description so that it includes eigenmatrices of the extended Cartan matrices of types B , C , F , and G .