Ilia Binder,Department of Mathematics, University of Toronto, Bahen Centre, 40 St. George St., Toronto, Ontario, Canada M5S 2E4;
e-mail: ilia@math.toronto.edu

David Damanik,Department of Mathematics, Rice University, Houston, TX 77005, USA; e-mail: damanik@rice.edu

Milivoje Lukic,Department of Mathematics, Rice University, Houston, TX 77005, USA; e-mail: milivoje.lukic@rice.edu

Tom VandenBoom,Department of Mathematics, Rice University, Houston, TX 77005, USA; e-mail: tvandenboom@rice.edu

Abstract/Résumé:

We study an initial value problem for the Toda lattice with almost periodic initial data. We consider initial data for which the associated Jacobi operator is absolutely continuous and has a spectrum satisfying a Craig-type condition, and show the boundedness and almost periodicity in time and space of solutions.

On étudie un problème de Cauchy pour le système Toda avec des conditions initiales presque périodiques. On considère des conditions initiales pour lesquelles l’opérateur de Jacobi associé est absolument continu et a un spectre qui satisfait à une condition à la façon de Craig, afin de montrer que les solutions sont bornées et presque périodiques dans la variable spatiale aussi que temporelle.

Keywords: Toda lattice, almost periodic Jacobi operators

AMS Subject Classification: Almost periodic solutions, Completely integrable systems; integrability tests; bi-Hamiltonian structures; hierarchies (KdV; KP; Toda; etc.), Jacobi (tridiagonal) operators (matrices) and generalizations 35B15, 37K10, 47B36

PDF(click to download): Almost Periodicity in Time of Solutions of the Toda Lattice

Nathan Grieve,Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB,Canada E3B 5A3; e-mail: n.grieve@unb.ca

Abstract/Résumé:

We study the infinite wedge representation and show how it is related to the universal central extension of \(g[t,t^{-1}]\), the loop algebra of a complex semi-simple Lie algebra \(g\). We also give an elementary proof of the boson-fermion correspondence. Our approach to proving this result is based on a combinatorial construction combined with an application of the Murnaghan-Nakayama rule.

Nous étudions l’algèbre extérieure en dimension infinie et montrons comment elle est reliée à l’extension centrale universelle de \(g[t,\!t^{-1}]\), l’algèbre de lacets sur une algèbre de Lie \(g\) semi-simple complexe. De plus, nous donnons une preuve élémentaire de la correspondance boson-fermion. Pour ce faire, nous utilisons une construction combinatoire, ainsi que la règle de Murnaghan-Nakayama.

Keywords: Boson-fermion correspondence, Infinite wedge representation, Murnaghan-Nakayama rule

AMS Subject Classification: Symmetric functions, Completely integrable systems; integrability tests; bi-Hamiltonian structures; hierarchies (KdV; KP; Toda; etc.) 05E05, 37K10

PDF(click to download): Comments Related to Infinite Wedge Representations