Algebraic analysis of solvable lattice models by Michio Jimbo and Tetsuji Miwa

By Michio Jimbo and Tetsuji Miwa

In keeping with the NSF-CBMS neighborhood convention lectures awarded via Miwa in June 1993, this e-book surveys fresh advancements within the interaction among solvable lattice versions in statistical mechanics and illustration idea of quantum affine algebras. simply because leads to this topic have been scattered within the literature, this e-book fills the necessity for a scientific account, focusing recognition on basics with no assuming previous wisdom approximately lattice types or illustration conception. After a quick account of uncomplicated rules in statistical mechanics, the authors speak about the normal matters bearing on solvable lattice versions in statistical mechanics, the most examples being the spin $1/2$ XXZ chain and the six-vertex version. The ebook is going directly to introduce the most items of analysis, the nook move matrices and the vertex operators, and discusses a few of their features from the point of view of physics. as soon as the actual motivations are in position, the authors go back to the math, overlaying the Frenkel-Jing bosonization of a undeniable module, formulation for the vertex operators utilizing bosons, the function of illustration concept, and correlation features and shape components. The restrict of the $XXX$ version is in brief mentioned, and the ebook closes with a dialogue of alternative forms of types and comparable works.

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