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Quantum Topology

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Volume 8, Issue 1, 2017, pp. 1–33
DOI: 10.4171/QT/85

Published online: 2017-03-23

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

Eric C. Rowell[1] and Hans Wenzl[2]

(1) Texas A&M University, College Station, USA
(2) University of California at San Diego, La Jolla, USA

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.

Keywords: Braid group, quantum group, spin representation, quantum torus

Rowell Eric, Wenzl Hans: SO$(N)_2$ braid group representations are Gaussian. Quantum Topol. 8 (2017), 1-33. doi: 10.4171/QT/85