Graded representations of the Temperley–Lieb algebra, quantum supergroups, and the Jones polynomial

DOI10.1063/1.529105zbMath0751.17017OpenAlexW2012062374MaRDI QIDQ3987291

Ruibin Zhang

Publication date: 28 June 1992

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.529105

zbMATH Keywords

irreducible representationsLie superalgebrasJones polynomialTemperley-Lieb algebraquantum supergroupgraded representationsgraded Yang-Baxter equation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Groups and algebras in quantum theory (81R99) Superalgebras (17A70)

Related Items

BETHE ANSATZ SOLUTION OF THE ANISOTROPIC CORRELATED ELECTRON MODEL ASSOCIATED WITH THE TEMPERLEY–LIEB ALGEBRA, Representation of complex number imaginary unit and supermatrix solution to the Yang-Baxter equation, Composite link polynomials from super Chern-Simons theory, Graded cellular bases for Temperley-Lieb algebras of type A and B, Braid group representations arising from quantum supergroups with arbitrary q and link polynomials, On the \mathcal {U}_{q}[sl(2) Temperley–Lieb reflection matrices], Temperley–LiebK-matrices, On the \(\mathcal{{U}}_{q}[osp(1|2)\) Temperley-Lieb model], Two variable link polynomials from quantum supergroups, Quantum Yang-Baxter equation and constantR-matrix over Grassmann algebra, Baxterization of the \(R\)-matrix for the adjoint representation of \(U_ q[D(2,1; {\alpha{}})\)], Exact solutions of graded Temperley-Lieb Hamiltonians.

Cites Work

• Solutions of the classical Yang-Baxter equation for simple superalgebras
• Solutions of the Yang-Baxter equation
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• State models and the Jones polynomial
• Trigonometric solutions of triangle equations. Simple Lie superalgebras
• Quantum group invariants and link polynomials
• Quantum Lie superalgebras and q-oscillators
• QUANTUM SUPERGROUPS AND SOLUTIONS OF THE YANG-BAXTER EQUATION
• Temperley-Lieb lattice models arising from quantum groups
• Relations between the ‘percolation’ and ‘colouring’ problem and other graph-theoretical problems associated with regular planar lattices: some exact results for the ‘percolation’ problem
• Lie superalgebras