On Ocneanu's theory of double triangle algebras for subfactors and classification of irreducible connections on the Dynkin diagrams |
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Authors: | Satoshi Goto |
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Institution: | Department of Mathematics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan |
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Abstract: | We give an exposition of Ocneanu's theory of double triangle algebras for subfactors and its application to the classification of irreducible bi-unitary connections on the Dynkin diagrams An, Dn, E6, E7 and E8. More precisely, we give a detailed proof of the complete classification of irreducible K–L bi-unitary connections up to gauge choice, where K and L represent the two horizontal graphs which are among the A–D–E Dynkin diagrams. The result also provides a simple proof of the flatness of D2n, E6 and E8 connections as well as an easy computation of the flat part of E7 as an application. |
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Keywords: | Subfactor Bi-unitary connection Dynkin diagram Double triangle algebra Fusion rule |
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