Free fermions and the Alexander-Conway polynomial

DOI10.1007/BF02101508zbMath0751.57004MaRDI QIDQ1181846

Hubert Saleur, Louis H. Kauffman

Publication date: 27 June 1992

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

zbMATH Keywords

quantum groupsknot theoryBurau representationbraid groupquantum deformationsfree fermionsBerezin integralConway-Alexander polynomialfundamental group of the complement of a knotstate model for the Alexander polynomial

Mathematics Subject Classification ID

Related Items (41)

First quantization of braided Majorana fermions ⋮ Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant ⋮ A non-commutative formula for the colored Jones function ⋮ Toward \(\mathrm {U}(N|M)\) knot invariant from ABJM theory ⋮ On the Hopf structure of \(U_{p,q}(\text{gl}(1| 1))\) and the universal \(\mathcal{T}\)-matrix of \(\text{Fun}_{p,q}(\text{GL}(1| 1))\) ⋮ Khovanov-Seidel quiver algebras and Ozsváth-Szabó's bordered theory ⋮ A new symmetry of the colored Alexander polynomial ⋮ Composite link polynomials from super Chern-Simons theory ⋮ The universal \(R\)-matrix, Burau representation, and the Melvin-Morton expansion of the colored Jones polynomial ⋮ Generalisations of Hecke algebras from loop braid groups ⋮ Other quantum relatives of the Alexander polynomial through the Links-Gould invariants ⋮ Chern-Simons theory in the temporal gauge and knot invariants through the universal quantum R-matrix ⋮ DG structures on odd categorified quantum \(sl(2)\) ⋮ Evaluations of link polynomials and recent constructions in Heegaard Floer theory ⋮ Non‐semisimple Levin–Wen models and Hermitian TQFTs from quantum (super)groups ⋮ Nonstandard quantum groups and superization ⋮ Ozsváth-Szabó bordered algebras and subquotients of category \(\mathcal{O} \) ⋮ The canonical partition function for quons ⋮ \(\text{gl}(N,N)\) current algebras and topological field theories ⋮ A closed formula for the evaluation of foams ⋮ Mixed quantum skew Howe duality and link invariants of type \(A\) ⋮ On the decategorification of Ozsváth and Szabó's bordered theory for knot Floer homology ⋮ Quantum and super-quantum group related to the Alexander-Conway polynomial ⋮ On integrable quantum group invariant antiferromagnets ⋮ Two variable link polynomials from quantum supergroups ⋮ The Alexander polynomial as quantum invariant of links ⋮ Quantum relatives of the Alexander polynomial ⋮ An oriented state model for the Jones polynomial and its applications alternating links ⋮ A novel symmetry of colored HOMFLY polynomials coming from \(\mathfrak{sl}(N|M)\) superalgebras ⋮ A categorification of \(\mathbf{U}_T(\mathfrak{sl}(1|1))\) and its tensor product representations ⋮ Modified quantum dimensions and re-normalized link invariants ⋮ Polynomial link invariants and quantum algebras ⋮ Three-dimensional \(BF\) theories and the Alexander-Conway invariant of knots ⋮ Spin chains viewed as the fermionic parts of supersymmetric quantum mechanical models. ⋮ Quantum Invariants of Templates ⋮ A topological interpretation of Viro's \(\mathfrak{gl}(1|1)\)-Alexander polynomial of a graph ⋮ Infinitely many two-variable generalisations of the Alexander-Conway polynomial ⋮ ALL LINK INVARIANTS FOR TWO DIMENSIONAL SOLUTIONS OF YANG–BAXTER EQUATION AND DRESSINGS ⋮ A quantum categorification of the Alexander polynomial ⋮ DUALITY IN osp(1|2) CONFORMAL FIELD THEORY AND LINK INVARIANTS ⋮ Invariance and the knot Floer cube of resolutions

Cites Work

• Solutions of the Yang-Baxter equation
• Universal R-matrix of the quantum superalgebra osp(2\(| 1)\)
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum R matrix for the generalized Toda system
• A polynomial invariant of oriented links
• State models and the Jones polynomial
• Hecke algebra representations of braid groups and link polynomials
• The Yang-Baxter equation and invariants of links
• Quantum field theory and the Jones polynomial
• A duality theorem for Reidemeister torsion
• A classifying invariant of knots, the knot quandle
• Quantum Lie superalgebras and q-oscillators
• A sketch of Lie superalgebra theory
• The theory of Lie superalgebras. An introduction
• Graded solutions of the Yang-Baxter relation and link polynomials
• A polynomial invariant for knots via von Neumann algebras
• Diagram and superfield techniques in the classical superalgebras
• FERMIONS AND LINK INVARIANTS
• An Invariant of Regular Isotopy
• Knot Invariants and the Critical Statistical Systems

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