JournalsqtVol. 11, No. 3pp. 489–524

Prime decomposition of modular tensor categories of local modules of type D

  • Andrew Schopieray

    Interlochen, USA
Prime decomposition of modular tensor categories of local modules of type D cover

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Abstract

Let C(g,k)\mathcal{C}(\mathfrak{g},k) 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 g\mathfrak{g} and positive integer levels kk. Here we classify nondegenerate fusion subcategories of the modular tensor categories of local modules C(g,k)R0\mathcal{C}(\mathfrak{g},k)_R^0 where RR is the regular algebra of Tannakian Rep(H)C(g,k)pt(H)\subset\mathcal{C}(\mathfrak{g},k)_\text{pt}. We describe the decomposition of C(g,k)R0\mathcal{C}(\mathfrak{g},k)_R^0 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 C(so5,k)\mathcal{C}(\mathfrak{so}_5,k) and C(g2,k)\mathcal{C}(\mathfrak{g}_2,k) for kZ1k\in\mathbb{Z}_{\geq1}.

Cite this article

Andrew Schopieray, Prime decomposition of modular tensor categories of local modules of type D. Quantum Topol. 11 (2020), no. 3, pp. 489–524

DOI 10.4171/QT/140