Hecke algebras, modular categories and 3-manifolds quantum invariants (Q1806120)

Modular categories are constructed from Hecke algebras at roots of unity, recovering, for a special choice of the framing parameter, the Reshetikhin-Turaev invariants of closed 3-manifolds constructed from the quantum groups \(U_qsl(N)\). The choice of framing parameter leads, for any rank \(N\) and level \(K\), to a modular category and a reduced invariant. If \(N\) and \(K\) are coprime, this recovers the \(PSU(N)\)-invariants; if \(N\) and \(K\) are not coprime it is shown that the reduced invariant admits spin and cohomological refinements, and a decomposition formula is proved extending a theorem of Murakami.