Related papers: Intertwining operators of the quantum Teichm\"ulle…
We start by describing how ideal triangulations on a surface degenerate under pinching of a multicurve. We use this process to construct a homomorphism from the Ptolemy groupoid of a surface to that of a pinched surface which is natural…
Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the theory of…
Intertwining relations for $N$-particle Calogero-like models with internal degrees of freedom are investigated. Starting from the well known Dunkl-Polychronakos operators, we construct new kind of local (without exchange operation)…
We describe a family of representations of $\pi_1(\Sigma)$ in PU(2,1), where $\Sigma$ is a hyperbolic Riemann surface with at least one deleted point. This family is obtained by a bending process associated to an ideal triangulation of…
Let $X$ be a rational homogeneous space and let $QH^*(X)_{loc}^\times$ be the group of invertible elements in the small quantum cohomology ring of $X$ localised in the quantum parameters. We generalise results of arXiv:math/0609796 and…
We study the general twisted intertwining operators (intertwining operators among twisted modules) for a vertex operator algebra $V$. We give the skew-symmetry and contragredient isomorphisms between spaces of twisted intertwining operators…
We establish an identification between the spaces of $\alpha$-fusion trees in non-semisimple topological quantum computation (NSS TQC) and a family of homological representations of the braid group known as the Lawrence representations…
Based on local unitary operators acting on a n-dimensional Hilbert-space, we investigate selective and collective operator basis sets for N-particle quantum networks. Selective cluster operators are used to derive the properties of general…
We construct continuously parametrised families of conformally invariant boundary operators on densities. These may also be viewed as conformally covariant boundary operators on functions and generalise to higher orders the first-order…
We characterize the Garsia-Rodemich spaces associated with a rearrangement invariant space via local maximal operators. Let $Q_{0}$ be a cube in $R^{n}$. We show that there exists $s_{0}\in(0,1),$ such that for all $0<s<s_{0},$ and for all…
In this paper we study twisted traces of products of intertwining operators for quantum affine algebras. They are interesting special functions, depending on two weights lambda, mu, three scalar parameters q, omega, k, and spectral…
We review recent progress in understanding the notion of locality in integrable quantum lattice systems. The central concept are the so-called quasilocal conserved quantities, which go beyond the standard perception of locality. Two…
We investigate the characters of some finite-dimensional representations of the quantum affine algebras $U_q(\hat{g})$ using the action of the copy of $U_q(g)$ embedded in it. First, we present an efficient algorithm for computing the…
In this paper, a geometric process to compare solutions of symmetric hyperbolic systems on (possibly different) globally hyperbolic manifolds is realized via a family of intertwining operators. By fixing a suitable parameter, it is shown…
We study the higher spin anologs of the six vertex model on the basis of its symmetry under the quantum affine algebra $U_q(\slth)$. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer…
We discuss applications of the $q$-characters to the computation of the $R$-matrices. In particular, we describe the $R$-matrix acting in the tensor square of the first fundamental representation of E$_8$ and in a number of other cases,…
This is a commentary on Teichm\"ullers' paper "Ver\"anderliche Riemannsche Fl\"achen" (Variable Riemann Surfaces), published in 1944. This paper is the last one that Teichm\"uller wrote on the problem of moduli. At most places the paper…
We sharpen the orbit method for finite groups of small nilpotence class by associating representations to functionals on the corresponding Lie rings. This amounts to describing compatible intertwiners between representations parameterized…
We prove a general criterion for a von Neumann algebra $M$ in order to be in standard form. It is formulated in terms of an everywhere defined, invertible, antilinear, a priori not necessarily bounded operator, intertwining $M$ with its…
A finite dimensional operator that commutes with some symmetry group admits quotient operators, which are determined by the choice of associated representation. Taking the quotient isolates the part of the spectrum supporting the chosen…