Y-systems and generalized associahedra I
refreshments at 3:45pm
This is the first of two talks based on a joint paper
with Sergey Fomin. I will concentrate on Y-systems, a particular class of
birational recurrence relations associated with an arbitrary finite root
system. These relations were introduced in 1991 by Al.B.Zamolodchikov,
in connection with the theory of thermodynamic Bethe ansatz.
We prove Zamolodchikov's conjecture that this system exhibits
periodicity with period h+2, where h is the Coxeter number of
the root system. Our proof is based on the study of a piecewise-linear
version of the Y-system obtained from it by the "tropicalization"
procedure. This version allows us to introduce a new family of simple
polytopes (generalized associahedra) associated with root systems.
These polytopes will be discussed by Sergey Fomin in the second talk
of this series.
Speaker's Contact Info: andrei(at-sign)neu.ed
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