Drinfeld–Sokolov hierarchies, tau functions, and generalized Schur polynomials - Université d'Angers Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

Drinfeld–Sokolov hierarchies, tau functions, and generalized Schur polynomials

Résumé

For a simple Lie algebra g and an irreducible faithful representation π of g, we introduce the Schur polynomials of (g, π)-type. We then derive the Sato–Zhou type formula for tau functions of the Drinfeld–Sokolov (DS) hierarchy of g-type. Namely, we show that the tau functions are linear combinations of the Schur polynomials of (g, π)-type with the coefficients being the Plücker coordinates. As an application, we provide a way of computing polynomial tau functions for the DS hierarchy. For g of low rank, we give several examples of polynomial tau functions, and use them to detect bilinear equations for the DS hierarchy.
Fichier principal
Vignette du fichier
1709.07309.pdf (231.47 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01593128 , version 1 (25-09-2017)

Identifiants

  • HAL Id : hal-01593128 , version 1

Citer

Mattia Cafasso, Ann Du Crest de Villeneuve, Di Yang. Drinfeld–Sokolov hierarchies, tau functions, and generalized Schur polynomials. 2017. ⟨hal-01593128⟩
156 Consultations
349 Téléchargements

Partager

Gmail Facebook X LinkedIn More