IRREDUCIBILITY OF SOME QUANTUM REPRESENTATIONS OF MAPPING CLASS GROUPS

DOI10.1142/S021821650100113XzbMath1001.57036arXivmath/9909128OpenAlexW2005330199MaRDI QIDQ4541041

Justin Roberts

Publication date: 30 July 2002

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9909128

zbMATH Keywords

TQFT

Mathematics Subject Classification ID

Related Items (17)

Representations of the Kauffman bracket skein algebra. I: Invariants and miraculous cancellations ⋮ Irreducibility of quantum representations of mapping class groups with boundary ⋮ Decomposition of some Witten-Reshetikhin-Turaev representations into irreducible factors ⋮ Reducibility of quantum representations of mapping class groups ⋮ Profinite completions of Burnside-type quotients of surface groups ⋮ On the (in)finiteness of the image of Reshetikhin-Turaev representations ⋮ Irreducible factors of modular representations of mapping class groups arising in integral TQFT ⋮ Applications of quantum representations of mapping class groups ⋮ Mapping class group representations and Morita classes of algebras ⋮ Embedding quantum PSU(2) representations of SL ₂ (ℤ) in quantum PSU(3) representations ⋮ Dimension formulas for some modular representations of the symplectic group in the natural characteristic. ⋮ Hitchin's connection, Toeplitz operators, and symmetry invariant deformation quantization ⋮ SO(3) quantum invariants are dense ⋮ Positivity of the universal pairing in 3 dimensions ⋮ Density of the \(\text{SO}(3)\) TQFT representation of mapping class groups ⋮ The Witten-Reshetikhin-Turaev representation of the Kauffman bracket skein algebra ⋮ Notes on Topological Quantum Field Theories

Cites Work

• The A-D-E classification of minimal and \(A_ 1^{(1)}\) conformal invariant theories
• On the TQFT representations of the mapping class groups
• Skein theory and Turaev-Viro invariants
• Topological quantum field theories derived from the Kauffman bracket
• Invariants of 3-manifolds via link polynomials and quantum groups
• Integral modular categories and integrality of quantum invariants at roots of unity of prime order
• On the Witten-Reshetikhin-Turaev representations of mapping class groups
• THE SKEIN METHOD FOR THREE-MANIFOLD INVARIANTS
• Skeins and mapping class groups
• A simple proof of integrality of quantum invariants at prime roots of unity

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