# Drinfeld-Sokolov Hierarchies, Tau Functions, and Generalized Schur Polynomials

Abstract : 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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Journal articles

https://hal.archives-ouvertes.fr/hal-02067010
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Submitted on : Wednesday, March 13, 2019 - 9:27:37 PM
Last modification on : Wednesday, October 23, 2019 - 5:15:35 AM

### Citation

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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