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20 April 2024
 
  » arxiv » 1506.5378

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Zamolodchikov integrability via rings of invariants
Pavlo Pylyavskyy ;
Date 17 Jun 2015
AbstractZamolodchikov periodicity is periodicity of certein recursions associated with box products X square Y of two finite type Dynkin diagrams. We suggest an affine analog of Zamolodchikov periodicity, which we call Zamolodchikov integrability. We conjecture that it holds for products X square Y, where X is a finite type Dynkin diagram and Y is an extended Dynkin diagram. We prove this conjecture for the case of A_m square A_{2n-1}^{(1)}. The proof employs cluster structures in certain classical rings of invariants, previously studied by S.~Fomin and the author.
Source arXiv, 1506.5378
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