06/C257

 

Estudio de simetrías y dualidades en sistemas integrables clásicos y cuánticos

Symmetries and dualities in classical and quantum integrable systems

 

Director: MONTANI, Hugo Santos

Correo electrónico: montani@cab.cnea.gov.ar

 

Co-Director: TRINCHERO, Roberto Carlos

 

Integrantes: CAPRIOTTI, Santiago; BARBEIRA, Alvaro Numa; NIKLISON, Matías

 

Resumen Técnico: El resumen técnico tiene por objetivo la aprehensión sintética de su proyecto, será almacenado en el sistema computarizado de la Secretaría de Ciencia, Técnica y Posgrado debe permitir el fácil acceso a la información. Haga una síntesis de los objetivos, la línea de investigación, la hipótesis de trabajo, la metodología, producto a obtener, sistema de transferencia y beneficios esperados. De ninguna manera debe exceder el espacio disponible en el formulario.

 

Summary: In this project we shall be concerned with the study of geometric and algebraic aspects of classical and quantum integrable systems. Symplectic and Poisson geometry of Hamiltonian systems will provide the main framework for dealing with classical issues, mainly for those phase spaces on the cotangent bundle of a Poisson-Lie group. We shall work on the extension of the T-duality scheme developed for Drinfeld doubles to the Iwasawa decomposition of some semisimple Lie group. This involves many aspects of the geometry and dynamics of systems of this type. Our approach will be addressed to manage the constraints structure. The main example are the loop groups which turn to be 1+1 conformal field theories. The states space of a quantum integrable system can be characterized as the representation space of some algebra of observable operators, which in this case can be encoded in a Hopf or weak Hopf algebra structure. In the conformal case, the main subject is to unveil the relation of these algebraic structures with those of Kac-Moody and Virasoro algebras. The properties of the category of modules of these algebras is determined from the symmetries of the graph associated to semisimple Lie algebras and the geometry of paths on them. The reciprocal problem, the reconstruction of the algebraic object is made in the framework of the Tannaka-Krein reconstruction theorem.