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Polynomial tau functions and bilinearization of the Drinfeld–Sokolov hierarchies

Le : 16/01/2018 14h00
Par : Ann du Crest de Villeneuve (LAREMA)
Lieu : i001
Lien web :
Résumé : In 1985, Drinfeld and Sokolov showed how to associate a sequence of integrable PDEs to any semi-simple Lie algebra, now called the Drinfeld--Sokolov hierarchies. One of their important features is the tau-symmetry property that ensures the existence of a single function, called the tau function, such that the components of a solution to the hierarchy are the logarithmic derivatives of the tau function. In this talk, I aim to describe how to compute polynomial tau functions via Sato's Grassmannian approach and Toeplitz determinants and give some examples and applications to the bilinearization of the hierarchies.