Let Uq(Ĝ) be a quantized affine Lie algebra. It is proven that the universal R-matrix R of Uq(Ĝ) satisfies the celebrated conjugation relation R = TR with T the usual twist map. As applications, braid generators are shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight Uq(Ĝ)-module and a spectral decomposition formula for the braid generators is...

An affine transformation on the plane is a mapping T that preserves collinearity and ratios of distances: given two points A and B, if C is the middle of the segment [A,B] then T (C) is the middle of the segment [T (A), T (B)]. Translations, contractions, expansions, reflections, rotations, are all particular cases of affine transformations. In general, an affine transformation T maps a point (...

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

This paper presents a methodology for historical map registration with a multi-image affine transformation estimated with a simultaneous Least Squares independent model adjustment. The method is based on two set of equations for (i) image-to-ground and (ii) image-to-image points and provides the rectification parameters with a global approach where all the unknowns are simultaneously estimated....

of Prof. Yau's lecture, Monday, April 2 [with additional references and remarks] (for people who missed the lecture) A geometric structure on a manifold is a cover by coordinate systems [a " sub-atlas " ] in which the transition functions from one coordinate system to another are not arbitrary mappings but rather belong to some specific set of mappings from (open subsets of) Euclidean space to ...

We show that an affine-invariant code C of length p is not permutation equivalent to a cyclic code except in the obvious cases: m = 1 or C is either {0}, the repetition code or its dual. Affine-invariant codes were firstly introduced by Kasami, Lin and Peterson [KLP2] as a generalization of Reed-Muller codes. This class of codes has received the attention of several authors because of its good ...

This paper provides a survey for the latest developments in the theory of affine q-Schur algebras and Schur–Weyl duality between affine quantum gln and affine type A Hecke algebras. More precisely, we will establish, on the one side, an isomorphism between the double Ringel–Hall algebra D△(n) of a cyclic quiver △(n) and the quantum loop algebra of gln, and establish, on the other side, explicit...

This paper is concerned with kinematically asymmetrically affine control systems with nonholonomic affine constraints (KAACS). We first show the nonintegrability condition for affine constraints using their geometric representation. Next, the KAACS is uniquely derived from affine constraints and control inputs. We then analyze the KAACS based on nonlinear control theory and provide some conditi...

In secret quantum communications the best eavesdropping attacks on quantum cryptography are based on imperfect cloning machines. The incoherent attack, based on quantum cloning, is the most common eavesdropping strategy. Using a probe, the eavesdropper imperfectly clones the sender’s quantum state which keeps one copy and sends the other. The physically allowed transformations of Eve’s quantum ...

We need some definitions from [1]. Let C ⊂ R2 be a convex body. A chord pq of C is called an affine diameter of C, if there is no longer parallel chord in C. The ratio of |ab| to 1 2 |a′b′|, where a′b′ is an affine diameter of C parallel to ab, is called the C-length of ab, or the relative length of ab, if there is no doubt about C. We denote it by λC(ab). Denote by λn the relative length of a ...