Jones-Wenzl idempotents for rank 2 simple Lie algebras

zbMath1133.57008arXivmath/0602504MaRDI QIDQ2465255

Dong Seok Kim

Publication date: 9 January 2008

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0602504

zbMATH Keywords

Jones-Wenzlsingle clasp expansionsweb spaces

Mathematics Subject Classification ID

Topological quantum field theories (aspects of differential topology) (57R56)

Related Items

The one-row-colored 𝔰𝔩3 Jones polynomials for pretzel links ⋮ Triple clasp formulas for \(C_2\) webs ⋮ Skein and cluster algebras of unpunctured surfaces for \({\mathfrak{sl}}_3\) ⋮ \(A_2\)-planar algebras. II: Planar modules ⋮ Ferromagnetic ordering of energy levels for \(\mathrm{U}_q(\mathfrak{sl}_2)\) symmetric spin chains ⋮ A categorification of quantum \(\mathfrak{sl}_3\) projectors and the \(\mathfrak{sl}_3\) Reshetikhin-Turaev invariant of tangles ⋮ Twist formulas for one-row colored \(A_2\) webs and \(\mathfrak{sl}_3\) tails of \((2,2m)\)-torus links ⋮ Skein theory for the \(D_{2n}\) planar algebras ⋮ The 𝔰𝔩3 colored Jones polynomials for 2-bridge links

Uses Software

• PSTricks

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum field theory and the Jones polynomial
• The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\)
• Web bases for \(\text{sl}(3)\) are not dual canonical
• 3-valent graphs and the Kauffman bracket
• Skeins and quantum \(SU(N)\) invariants of 3-manifolds
• Canonical bases in tensor products and graphical calculus for \(U_ q(sl_ 2)\)
• Quantum invariants and finite group actions on three-manifolds.
• Homfly polynomial via an invariant of colored plane graphs
• The quantum \(SU(3)\) invariant of links and Murasugi's congruence
• \(\text{sl}(3)\) link homology
• Ribbon graphs and their invariants derived from quantum groups
• Index for subfactors
• Spiders for rank 2 Lie algebras
• Integrality and symmetry of quantum link invariants
• Invariants of 3-manifolds via link polynomials and quantum groups
• Skein theory for \(SU(n)\)-quantum invariants
• IS THE JONES POLYNOMIAL OF A KNOT REALLY A POLYNOMIAL?
• THE QUANTUM 𝔰𝔩(3) INVARIANTS OF CUBIC BIPARTITE PLANAR GRAPHS
• A polynomial invariant for knots via von Neumann algebras
• Distinct 3-Manifolds with all SU(2) q Invariants the Same
• THE SKEIN METHOD FOR THREE-MANIFOLD INVARIANTS
• THE QUANTUM G₂ LINK INVARIANT
• Quantum SU(3) Invariant of 3-Manifolds via Linear Skein Theory
• SOLUTIONS OF THE YANG-BAXTER EQUATION AND QUANTUM $\mathfrak{sl} (2)$
• CATEGORIFICATIONS OF THE COLORED JONES POLYNOMIAL
• Quantum invariants of periodic links and periodic 3-manifolds
• ASYMPTOTIC BEHAVIORS OF THE COLORED JONES POLYNOMIALS OF A TORUS KNOT
• Invariant tensors for the spin representation of (7)
• Matrix factorizations and link homology
• TRIHEDRON COEFFICIENTS FOR $\mathcal{U}_{q}(\mathfrak{sl}(3,\mathbb{C}))$
• Introduction to Lie Algebras and Representation Theory