82 citations · 651 across the 39 of their papers we have counts for
18 papers · 1 filter
Cylindric Hecke characters and Gromov-Witten invariants via the asymmetric six-vertex model
Christian Korff
We construct a family of infinite-dimensional positive sub-coalgebras within the Grothendieck ring of Hecke algebras, when viewed as a Hopf algebra with respect to the induction an…
Yang-Baxter algebras as convolution algebras: The Grassmannian case
Vassily Gorbounov, Christian Korff, Catharina Stroppel
We present a simple but explicit example of a recent development which connects quantum integrable models with Schubert calculus: there is a purely geometric construction of soluti…
From Quantum Bäcklund Transforms to Topological Quantum Field Theory
Christian Korff
We derive the quantum analogue of a Bäcklund transformation for the quantised Ablowitz-Ladik chain, a space discretisation of the nonlinear Schrödinger equation. The quantisation o…
Quantum cohomology via vicious and osculating walkers
Christian Korff
We relate the counting of rational curves intersecting Schubert varieties of the Grassmannian to the counting of certain non-intersecting lattice paths on the cylinder, so-called v…
Cylindric versions of specialised Macdonald functions and a deformed Verlinde algebra
Christian Korff
We define cylindric generalisations of skew Macdonald functions when one of their parameters is set to zero. We define these functions as weighted sums over cylindric skew tableaux…
The su(n) WZNW fusion ring as integrable model: a new algorithm to compute fusion coefficients
Christian Korff
This is a proceedings article reviewing a recent combinatorial construction of the su(n) WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit…
Noncommutative Schur polynomials and the crystal limit of the U_q sl(2)-vertex model
Christian Korff
Starting from the Verma module of U_q sl(2) we consider the evaluation module for affine U_q sl(2) and discuss its crystal limit (q=0). There exists an associated integrable statis…
PT Symmetry of the non-Hermitian XX Spin-Chain: Non-local Bulk Interaction from Complex Boundary Fields
Christian Korff
The XX spin-chain with non-Hermitian diagonal boundary conditions is shown to be quasi-Hermitian for special values of the boundary parameters. This is proved by explicit construct…
PT-invariance and representations of the Temperley-Lieb algebra on the unit circle
Christian Korff
We present in detail a recent conjecture on self-adjoint representations of the Temperley-Lieb algebra for particular values on the unit circle. The formulation in terms of graphic…
Turning the Quantum Group Invariant XXZ Spin-Chain Hermitian: A Conjecture on the Invariant Product
Christian Korff
This is a continuation of a previous joint work with Robert Weston on the quantum group invariant XXZ spin-chain (math-ph/0703085). The previous results on quasi-Hermiticity of thi…
PT Symmetry on the Lattice: The Quantum Group Invariant XXZ Spin-Chain
Christian Korff, Robert A. Weston
We investigate the PT-symmetry of the quantum group invariant XXZ chain. We show that the PT-operator commutes with the quantum group action and also discuss the transformation pro…
A Q-operator for the quantum transfer matrix
Christian Korff
Baxter's Q-operator for the quantum transfer matrix of the XXZ spin-chain is constructed employing the representation theory of quantum groups. The spectrum of this Q-operator is d…
A Q-operator for the twisted XXX model
Christian Korff
Taking the isotropic limit in a recent representation theoretic construction of Baxter's Q-operators for the XXZ model with quasi-periodic boundary conditions we obtain new results…
Solving Baxter's TQ-equation via representation theory
Christian Korff
Baxter's TQ-equation is solved for the six-vertex model using the representation theory of quantum groups at roots of unity. A novel simplified construction of the Q-operator is gi…
Auxiliary matrices on both sides of the equator
Christian Korff
The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show rema…
Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz
Christian Korff
We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calcu…
Auxiliary matrices for the six-vertex model at roots of unity II
Christian Korff
The spectra of recently constructed auxiliary matrices for the six-vertex model respectively the spin s=1/2 Heisenberg chain at roots of unity q^N=1 are investigated. Two conjectur…
Auxiliary matrices for the six-vertex model at roots of 1 and a geometric interpretation of its symmetries
Christian Korff
The construction of auxiliary matrices for the six-vertex model at a root of unity is investigated from a quantum group theoretic point of view. Employing the concept of intertwine…