Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials
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 Plu
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https://hal.science/hal-02067010
Soumis le : mercredi 13 mars 2019-21:27:37
Dernière modification le : vendredi 26 avril 2024-16:41:49
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Identifiants
- HAL Id : hal-02067010 , version 1
- DOI : 10.3842/SIGMA.2018.104
- INSPIRE : 1722418
Citer
Mattia Cafasso, Ann Du Crest De Villeneuve, Di Yang. Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials. SIGMA, 2018, 14, pp.104. ⟨10.3842/SIGMA.2018.104⟩. ⟨hal-02067010⟩
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