# SO$(N)_2$ 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

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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$(N)_2$ (for $N$ odd) and O$(N)_2$ (for $N$ even) in terms of quantum $(n-1)$-tori, via non-standard deformations of $U\mathfrak {so}_N$. 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$(N)_2$ braid group representations are Gaussian. Quantum Topol. 8 (2017), no. 1 pp. 1–33

DOI 10.4171/QT/85