Journal
JOURNAL OF HIGH ENERGY PHYSICS
Volume -, Issue 4, Pages -Publisher
SPRINGER
DOI: 10.1007/JHEP04(2021)299
Keywords
Global Symmetries; Space-Time Symmetries
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The article discusses a threefold classification and a tenfold classification scheme for unitary irreducible representations of groups, proving the equivalence of these two classification methods.
It is well-known that unitary irreducible representations of groups can be usefully classified in a 3-fold classification scheme: Real, Complex, Quaternionic. In 1962 Freeman Dyson pointed out that there is an analogous 10-fold classification of irreducible representations of groups involving both unitary and antiunitary operators. More recently, it was realized that there is also a 10-fold classification scheme involving superdivision algebras. Here we give a careful proof of the equivalence of these two 10-fold ways.
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