2008/06/30 by Siu-Hung Ng, Peter Schauenburg · 1 citation
Mathematics · Physics and Astronomy · #math.QA #hep-th #math-ph #math.CT #math.MP
paper · pdf · doi:10.1007/s00220-010-1096-6
published as Communications in Mathematical Physics, 300 (2010), no. 1, 1--46 · 42 pages Latex, corrected typos, added some references, slightly rewritten abstract of the previous version
arxiv created 2010/07/15 · arxiv updated 2012/02/07
We introduce generalized Frobenius-Schur indicators for pivotal categories. In a spherical fusion category C, an equivariant indicator of an object in C is defined as a functional on the Grothendieck algebra of the quantum double Z(C) via generalized Frobenius-Schur indicators. The set of all equivariant indicators admits a natural action of the modular group. Using the properties of equivariant indicators, we prove a congruence subgroup theorem for modular categories. As a consequence, all modular representations of a modular category have finite images, and they satisfy a conjecture of Eholzer. In addition, we obtain two formulae for the generalized indicators, one of them a generalization of Bantay's second indicator formula for a rational conformal field theory. This formula implies a conjecture of Pradisi-Sagnotti-Stanev, as well as a conjecture of Borisov-Halpern-Schweigert.