Y-systems and generalized associahedra I

Andrei Zelevinsky

Northeastern University

February 15,
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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Combinatorics Seminar, Mathematics Department, MIT, sara(at-sign)math.mit.edu

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