Representations of braid group obtained from rational conformal field theories can be used to obtain explicit representations of Temperley-Lieb-Jones algebras. The method is described in detail for SU(2) k Wess-Zumino conformal field theories and its generalization to an arbitrary rational conformal field theory outlined. Explicit definition of an associated linear trace operation in terms of a...

Abstract. The principal graph X of a subfactor with finite Jones index is one of the important algebraic invariants of the subfactor. If ∆ is the adjacency matrix of X we consider the equation ∆ = U + U. When X has square norm ≤ 4 the spectral measure of U can be averaged by using the map u → u, and we get a probability measure ε on the unit circle which does not depend on U . We find explicit ...

We study the polarisation properties of random N×N scattering matrices distributed according to circular orthogonal ensemble. interpret 2 × sub-blocks matrix as Jones and their statistical properties. Using polar decomposition, we derive probability density functions for retardance diattenuation from arbitrary size in limit N??.

The colored Jones function of a knot is a sequence of Laurent polynomials that encodes the Jones polynomial of a knot and its parallels. It has been understood in terms of representations of quantum groups and Witten gave an intrinsic quantum field theory interpretation of the colored Jones function as the expectation value of Wilson loops of a 3-dimensional gauge theory, the Chern-Simons theor...

Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by a linear system, and is dominated by finite type string link invariants. For positive string links, the representation matrix can be interpreted as the trans...

By performing radiation-damped R-matrix scattering calculations for the photorecombination of Fe forming Fe, we demonstrate and discuss the difficulties and fundamental inaccuracies associated with the R-matrix method for treating dielectronic recombination ~DR!. Our R-matrix results significantly improve upon earlier R-matrix results for this ion. However, we show theoretically that all R-matr...