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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01593128
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Submitted on : Monday, September 25, 2017 - 5:31:53 PM
Last modification on : Wednesday, November 3, 2021 - 9:18:35 AM
Long-term archiving on: : Tuesday, December 26, 2017 - 2:28:01 PM

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  • HAL Id : hal-01593128, version 1

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

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