$SO(N)_2$ Braid group representations are Gaussian Institutional Repository Document uri icon


  • We give a description of the centralizer algebras for tensor powers of spin objects in the pre-modular categories $SO(N)_2$ (for $N$ odd) and $O(N)_2$ (for $N$ even) in terms of quantum $(n-1)$-tori, via non-standard deformations of $Umathfrak{so}_N$. 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.

author list (cited authors)

  • Rowell, E. C., & Wenzl, H.

complete list of authors

  • Rowell, Eric C||Wenzl, Hans

Book Title

  • arXiv

publication date

  • January 2014