An expression of the multivariate sigma function associated with a (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of the sigma function is directly proved to be the Schur function determined from the gap sequence at infinity. ∗e-mail: [email protected]

Abstract We prove results for the study of double copy and tree-level colour/kinematics duality scattering amplitudes using properties Lie polynomials. show that ‘ S -map’ was defined to simplify super-Yang–Mills multiparticle superfields is in fact a bracket. A generalized KLT map from polynomials their dual obtained by studying our new bracket; matrix elements this yield recently proposed ‘ge...

It has been shown recently that extended supersymmetry in twisted firstorder sigma models is related to twisted generalized complex geometry in the target. In the general case there are additional algebraic and differential conditions relating the twisted generalized complex structure and the geometrical data defining the model. We study in the Hamiltonian formalism the case of vanishing metric...

We prove that the dualization algebra of the symmetric space coset sigma model is a Lie algebra and we show that it generates an appropriate adjoint representation which enables the local integration of the field equations yielding the first-order ones.

We construct the general algebraic curve of degree four solving the classical sigma model on R × S. Up to two loops it coincides with the algebraic curve for the dual sector of scalar operators in N = 4 SYM, also constructed here. We explicitly reproduce some particular solutions. Membre de l’Institut Universitaire de France

Abstract The pentagram map, introduced by Schwartz [The map. Exp. Math. 1 (1) (1992), 71–81], is a dynamical system on the moduli space of polygons in projective plane. Its real and complex dynamics have been explored detail. We study map over an arbitrary algebraically closed field characteristic not equal to 2. prove that twisted discrete integrable system, sense algebraic complete integrabil...

investigation of desertification trend needs understanding of phenomena creating changes singly or action and reaction together in the manner that these changes were ended up in land degradation. in investigation of pedological criterion onland degradation in quaternary rock units, first, a part of the rude-shoor watershed area was selected. after distinguishing target area, maps of slope class...