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arXiv · 1210.1888

Tensor diagrams and cluster algebras

Sergey Fomin·Pavlo Pylyavskyy
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Abstract

The rings of SL(V) invariants of configurations of vectors and linear forms in a finite-dimensional complex vector space V were explicitly described by Hermann Weyl in the 1930s. We show that when V is 3-dimensional, each of these rings carries a natural cluster algebra structure (typically, many of them) whose cluster variables include Weyl's generators. We describe and explore these cluster structures using the combinatorial machinery of tensor diagrams. A key role is played by the web bases introduced by G.Kuperberg.

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Sergey Fomin, Pavlo Pylyavskyy. 2015-05-18. Tensor diagrams and cluster algebras. https://arxiv.org/abs/1210.1888

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