Quantum Topology


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Published online first: 2018-07-26
DOI: 10.4171/QT/116

Irreducibility of quantum representations of mapping class groups with boundary

Thomas Koberda[1] and Ramanujan Santharoubane[2]

(1) University of Virginia, Charlottesville, USA
(2) University of Virginia, Charlottesville, USA

We prove that theWitten–Reshetikhin–Turaev SU(2) quantum representations of mapping class groups are always irreducible in the case of surfaces equipped with colored banded points, provided that at least one banded point is colored by 1. We thus generalize a well-known result due to J. Roberts.

Keywords: TQFT representation, curve operator, skein algebra, irreducible representation, point-pushing, Birman exact sequence

Koberda Thomas, Santharoubane Ramanujan: Irreducibility of quantum representations of mapping class groups with boundary. Quantum Topol. Electronically published on July 26, 2018. doi: 10.4171/QT/116 (to appear in print)