Q-system Cluster Algebras, Paths and Total Positivity
نویسندگان
چکیده
منابع مشابه
Q - system Cluster Algebras , Paths and Total Positivity ?
In the first part of this paper, we provide a concise review of our method of solution of the Ar Q-systems in terms of the partition function of paths on a weighted graph. In the second part, we show that it is possible to modify the graphs and transfer matrices so as to provide an explicit connection to the theory of planar networks introduced in the context of totally positive matrices by Fom...
متن کاملCluster Algebras , Paths and Total Positivity
We review the solution of the Ar Q-systems in terms of the partition function of paths on a weighted graph, and show that it is possible to modify the graphs and transfer matrices so as to provide an explicit connection to the theory of planar networks introduced in the context of totally positive matrices by Fomin and Zelevinsky. We also apply our method to give a simple solution for the rank ...
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This is a brief and informal introduction to cluster algebras. It roughly follows the historical path of their discovery, made jointly with A. Zelevinsky. Total positivity serves as the main motivation. Mathematics Subject Classification (2000). Primary 13F60, Secondary 05E10, 05E15, 14M15, 15A23, 15B48, 20F55, 22E46.
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Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili [Kadomtsev BB, Petviashvili VI (1970) Sov Phys Dokl 15:539-541] proposed a two-dimensional nonlinear dispersive wave equation now known as the KP equation. It is well-known that the Wronskian approach to the KP equation provides a method to construct soliton solutions. The regular soliton solution...
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These are notes from introductory survey lectures given at the Institute for Studies in Theoretical Physics and Mathematics (IPM), Teheran, in 2008 and 2010. We present the definition and the fundamental properties of Fomin-Zelevinsky’s cluster algebras. Then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generator...
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ژورنال
عنوان ژورنال: Symmetry, Integrability and Geometry: Methods and Applications
سال: 2010
ISSN: 1815-0659
DOI: 10.3842/sigma.2010.014