Zamolodchikov integrability via rings of invariants

2015/06/17 by Pylyavskyy, Pavlo
#05E10 #13F60 #15A72 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1506.05378

Abstract

Zamolodchikov 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.

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