University of Birmingham > Talks@bham > Geometry and Mathematical Physics seminar > Tau functions of the Drinfeld–Sokolov hierarchies and Schur polynomials

Tau functions of the Drinfeld–Sokolov hierarchies and Schur polynomials

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If you have a question about this talk, please contact Andrea Brini.

The Drinfeld–Sokolov hierarchies are sequences of evolution partial differential equations. They are associated, in particular, to any semisimple Lie algebra via its affine algebra. To any solution of these equations, one can define a tau function, often easier to compute. I will show how to compute tau functions by means of the limit of Toeplitz determinants, leading to an expansion of the tau function over integer partitions. This expansion involves generalizations of Schur polynomials to arbitrary semisimple Lie algebras and gives a simple condition for the polynomiality of the tau function. This a joint work with Mattia Cafasso (University of Angers, France) and Di Yang (USTC, Hefei, China).

This talk is part of the Geometry and Mathematical Physics seminar series.

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