Tropical representation of Weyl groups associated with certain rational varieties

Teruhisa Tsuda; Tomoyuki Takenawa

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Tropical representation of Weyl groups associated with certain rational varieties

Teruhisa Tsuda·Tomoyuki Takenawa

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Abstract

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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BibTeX RIS

Teruhisa Tsuda, Tomoyuki Takenawa. 2008-12-09. Tropical representation of Weyl groups associated with certain rational varieties. https://arxiv.org/abs/math/0607661

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