Klein Topological Field Theories from Group Representations

We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the represe...

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Bibliographic Details
Published in:Symmetry, integrability and geometry, methods and applications integrability and geometry, methods and applications, 2011-01, Vol.7, p.070
Main Author: Loktev, Sergey A.
Format: Article
Language:English
Subjects:
group representation
topological quantum field theory
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Summary:We show that any complex (respectively real) representation of finite group naturally generates a open-closed (respectively Klein) topological field theory over complex numbers. We relate the 1-point correlator for the projective plane in this theory with the Frobenius-Schur indicator on the representation. We relate any complex simple Klein TFT to a real division ring.
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2011.070