Communications in Mathematical Physics

, Volume 210, Issue 3, pp 733–784

Chiral Structure of Modular Invariants for Subfactors

  • Jens Böckenhauer
  • David E. Evans
  • Yasuyuki Kawahigashi

DOI: 10.1007/s002200050798

Cite this article as:
Böckenhauer, J., Evans, D. & Kawahigashi, Y. Comm Math Phys (2000) 210: 733. doi:10.1007/s002200050798

Abstract:

In this paper we further analyze modular invariants for subfactors, in particular the structure of the chiral induced systems of M-M morphisms. The relative braiding between the chiral systems restricts to a proper braiding on their “ambichiral” intersection, and we show that the ambichiral braiding is non-degenerate if the original braiding of the N-N morphisms is. Moreover, in this case the dimensions of the irreducible representations of the chiral fusion rule algebras are given by the chiral branching coefficients which describe the ambichiral contribution in the irreducible decomposition of α-induced sectors. We show that modular invariants come along naturally with several non-negative integer valued matrix representations of the original N-N Verlinde fusion rule algebra, and we completely determine their decomposition into its characters. Finally the theory is illustrated by various examples, including the treatment of all SU(2)k modular invariants.

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Jens Böckenhauer
    • 1
  • David E. Evans
    • 1
  • Yasuyuki Kawahigashi
    • 2
  1. 1.School of Mathematics, University of Wales, Cardiff, PO Box 926, Senghennydd Road, Cardiff CF24 4YH, Wales, UK. E-mail: BockenhauerJM@cf.ac.uk; EvansDE@cf.ac.ukUK
  2. 2.Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153-8914, Japan.¶E-mail: yasuyuki@ms.u-tokyo.ac.jpJP

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