On tensor products of positive representations of split real quantum Borel subalgebra $\mathcal {U}_{q\widetilde {q}}(\mathfrak {b}_\mathbb {R})$

DOI10.1090/tran/7110zbMath1385.81028arXiv1405.4786OpenAlexW2552673881MaRDI QIDQ4608774

Ivan Chi-Ho Ip

Publication date: 28 March 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.4786

zbMATH Keywords

GNS-representationquantum dilogarithmmodular doublehigher Teichmüller theorysplit real quantum groupspositive representations

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) (C^*)-algebras and (W^*)-algebras in relation to group representations (22D25) Hopf algebras and their applications (16T05)

Related Items (4)

Ratio coordinates for higher Teichmüller spaces ⋮ On tensor product decomposition of positive representations of \(\mathcal{U}_{q\widetilde{q}}(\mathfrak{sl}(2,\mathbb{R}))\) ⋮ Three-dimensional quantum gravity from the quantum pseudo-Kähler plane ⋮ Cluster realization of positive representations of a split real quantum Borel subalgebra

Cites Work

• Unnamed Item
• Unnamed Item
• Representation of the quantum plane, its quantum double, and harmonic analysis on \(GL_q^+(2,\mathbb{R })\)
• Quantum Teichmüller space from the quantum plane
• Correlation functions in conformal Toda field theory. I
• The quantum dilogarithm and representations of quantum cluster varieties
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum deformations of certain simple modules over enveloping algebras
• Quantum field theory and the Jones polynomial
• Quantization of Teichmüller spaces and the quantum dilogarithm
• R-operator, co-product and Haar-measure for the modular double of \(U_q(\mathfrak{sl}(2,\mathbb R))\).
• Ribbon graphs and their invariants derived from quantum groups
• Discrete Heisenberg-Weyl group and modular group
• Positive representations of non-simply-laced split real quantum groups
• Invariants of 3-manifolds via link polynomials and quantum groups
• An invitation to quantum groups and duality. From Hopf algebras to multiplicative unitaries and beyond
• Moduli spaces of local systems and higher Teichmüller theory
• Some remarks on Teichmüller's space of Riemann surfaces
• Noncommutative hypergeometry
• Unitaires multiplicatifs et dualité pour les produits croisés de $\mathrm{C}^*$-algèbres
• POSITIVE REPRESENTATIONS OF SPLIT REAL QUANTUM GROUPS
• Positive Representations of Split Real Quantum Groups and Future Perspectives
• Canonical Bases Arising from Quantized Enveloping Algebras
• QUANTUM DILOGARITHM
• Multiplier Hopf Algebras
• Positive representations, multiplier Hopf algebra, and continuous canonical basis
• Positive Representations of Split Real Quantum Groups: The Universal R Operator
• Quantization of moduli spaces of flat connections and Liouville theory
• Locally compact quantum groups
• A quantum Teichmüller space
• Clebsch-Gordan and Racah-Wigner coefficients for a continuous series of representations of \(\mathcal U_q(\mathfrak{sl}(2,\mathbb R))\)

This page was built for publication: On tensor products of positive representations of split real quantum Borel subalgebra $\mathcal {U}_{q\widetilde {q}}(\mathfrak {b}_\mathbb {R})$