Let be the unitary modular tensor categories arising from the representation theory of quantum groups at roots of unity for arbitrary simple finite-dimensional complex Lie algebra and positive integer levels . Here we classify nondegenerate fusion subcategories of the modular tensor categories of local modules where is the regular algebra of Tannakian Rep. We describe the decomposition of into prime factors, and as an application we classify relations in the Witt group of nondegenerately braided fusion categories generated by the equivalency classes of and for .
Cite this article
Andrew Schopieray, Prime decomposition of modular tensor categories of local modules of type D. Quantum Topol. 11 (2020), no. 3, pp. 489–524DOI 10.4171/QT/140