Tropical representation of Weyl groups associated with certain rational varieties

Content Provider	Semantic Scholar
Author	Tsuda, Teruhisa Takenawa, Tomoyuki
Copyright Year	2006
Abstract	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. We develop an algebro-geometric framework of τ -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.
Starting Page	936
Ending Page	954
Page Count	19
File Format	PDF HTM / HTML
DOI	10.1016/j.aim.2009.01.013
Volume Number	221
Alternate Webpage(s)	http://arxiv.org/pdf/math/0607661v3.pdf
Alternate Webpage(s)	https://export.arxiv.org/pdf/math/0607661
Alternate Webpage(s)	https://arxiv.org/pdf/math/0607661v3.pdf
Alternate Webpage(s)	http://arxiv.org/pdf/math/0607661v1.pdf
Alternate Webpage(s)	https://doi.org/10.1016/j.aim.2009.01.013
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article