arXiv · 0804.0274
We introduce the notion of abelian solutions of KP equations and show that all of them are algebro-geometric.
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I. Krichever, T. Shiota. 2008-04-02. Abelian solutions of the KP equation. https://arxiv.org/abs/0804.0274
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These notes were prepared for a series of intensive lectures delivered at Hokkaido University, Nagoya University, Kyoto University, and Kyushu University. We begin with a brief review of higher-form symmetries, anomalies, and discrete gauge theories, before introducing non-invertible symmetries in $(1+1)$-dimensional systems. The basic structure of fusion categories is then discussed, including a discussion of categorical analogs of discrete gauging and representation theory. We subsequently turn to $(3+1)$-dimensional theories, where several physical applications of non-invertible symmetries are discussed. These notes are intended to be largely self-contained, and require no prior familiarity with subjects such as conformal field theory or lattice models.
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