Reflection groups and discrete integrable systems

Discrete Moving Frames and Discrete Integrable Systems

Group-based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group-based moving frame, which is essentially a sequence of moving frames with overlapping domains. We demonstrate a small set of generators of the algebra of invariants, which...

Discrete Integrable Systems and Geometry

Normalization Factors, Reflection Amplitudes and Integrable Systems

We calculate normalization factors and reflection amplitudes in the Winvariant conformal quantum field theories. Using these CFT data we derive vacuum expectation values of exponential fields in affine Toda theories and related perturbed conformal field theories. We apply these results to evaluate explicitly the expectation values of order parameters in the field theories associated with statis...

Integrable Systems and Quantum Groups

The main purpose of this lecture is to present the study of quantum integrable systems and its interplay with the study of quantum groups. The history of quantum integrable systems begins, following a certain historical path, with the rst attempts of W. Heisenberg to develop a microscopic theory that could explain ferromagnetism [1]. Later on a method was proposed by H. Bethe [2] in order to ob...

Hyperdeterminants as integrable discrete systems

We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonlinear difference equation defined by the 2×2×2 hyperdeterminant. This result gives rise to the following hypothesis: the difference equations defined by hyperdeterminants of any size are integrable. We show that this ...