Tropical representation of Weyl groups associated with certain rational varieties

Details Tropical representation of Weyl groups associated with certain rational varieties Tropical representation of Weyl groups associated with certain rational varieties

2006-07-26

arxiv.org/abs/math/0607661v3

Mathematics

Algebraic Geometry

18 pages, 3 figures; corrected mainly in Sect.4 and 5

Scientific paper

Starting from certain rational varieties blown-up from (P^1)^N, we construct a tropical, i.e., subtraction-free birational, representation of Weyl groups as a group of pseudo isomorphisms of the varieties. Furthermore, we develop an algebro-geometric framework of tau-functions as defining functions of exceptional divisors on the varieties. In the case where the corresponding root system is of affine type, our construction yields a class of (higher order) q-difference Painleve equations and its algebraic degree grows quadratically.

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