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Pré-Publication, Document De Travail Année : 2018

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

Ann Du Crest de Villeneuve
  • Fonction : Auteur
Di Yang
  • Fonction : Auteur
  • PersonId : 994385

Résumé

For a simple Lie algebra $\mathfrak{g}$ and an irreducible faithful representation $\pi$ of $\mathfrak{g}$, we introduce the Schur polynomials of $(\mathfrak{g},\pi)$-type. We then derive the Sato-Zhou type formula for tau functions of the Drinfeld-Sokolov (DS) hierarchy of $\mathfrak{g}$-type. Namely, we show that the tau functions are linear combinations of the Schur polynomials of $(\mathfrak{g},\pi)$-type with the coefficients being the Pl\"ucker coordinates. As an application, we provide a way of computing polynomial tau functions for the DS hierarchy. For $\mathfrak{g}$ of low rank, we give several examples of polynomial tau functions, and use them to detect bilinear equations for the DS hierarchy.

Dates et versions

hal-01676243 , version 1 (05-01-2018)

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Mattia Cafasso, Ann Du Crest de Villeneuve, Di Yang. Drinfeld-Sokolov hierarchies, tau functions, and generalized Schur polynomials. 2018. ⟨hal-01676243⟩
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