JournalsqtVol. 8 , No. 1pp. 1–33

SO(N)2(N)_2 braid group representations are Gaussian

  • Eric C. Rowell

    Texas A&M University, College Station, USA
  • Hans Wenzl

    University of California at San Diego, La Jolla, USA
SO$(N)_2$ braid group representations are Gaussian cover
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Abstract

We give a description of the centralizer algebras for tensor powers of spin objects in the pre-modular categories SO(N)2(N)_2 (for NN odd) and O(N)2(N)_2 (for NN even) in terms of quantum (n1)(n-1)-tori, via non-standard deformations of UsoNU\mathfrak {so}_N. As a consequence we show that the corresponding braid group representations are Gaussian representations, the images of which are finite groups. This verifies special cases of a conjecture that braid group representations coming from weakly integral braided fusion categories have finite image.

Cite this article

Eric C. Rowell, Hans Wenzl, SO(N)2(N)_2 braid group representations are Gaussian. Quantum Topol. 8 (2017), no. 1 pp. 1–33

DOI 10.4171/QT/85