Higher Gauss sums of modular categories

• Siu-Hung Ng ^[1] ; Andrew Schopieray ^[2] ; Yilong Wang ^[1]
  1. [1] Louisiana State University

     Louisiana State University

     Estados Unidos

     
  2. [2] UNSW, Australia
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 4, 2019
• Idioma: inglés
• DOI: 10.1007/s00029-019-0499-2
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• Resumen

  • The definitions of the nth Gauss sum and the associated nth central charge are introduced for premodular categories \mathcal {C} and n\in \mathbb {Z}. We first derive an expression of the nth Gauss sum of a modular category \mathcal {C}, for any integer n coprime to the order of the T-matrix of \mathcal {C}, in terms of the first Gauss sum, the global dimension, the twist and their Galois conjugates. As a consequence, we show for these n, the higher Gauss sums are d-numbers and the associated central charges are roots of unity. In particular, if \mathcal {C} is the Drinfeld center of a spherical fusion category, then these higher central charges are 1. We obtain another expression of higher Gauss sums for de-equivariantization and local module constructions of appropriate premodular and modular categories. These expressions are then applied to prove the Witt invariance of higher central charges for pseudounitary modular categories.