English

Period 2 quivers and their T- and Y-systems

Mathematical Physics 2021-09-24 v1 Commutative Algebra Dynamical Systems math.MP

Abstract

We give a general definition for period 22 quivers before making some prudent assumptions to reduce the number of possibilities. Finding these quivers requires solving a complicated system of equations between the number of arrows in the quiver. We find all solutions of these systems for quivers with N=3,4,5N=3,4,5 vertices and give some solutions for N=6N=6. We then consider the TT- and YY-systems associated with these quivers, some of which exhibit periodic quantities which lead to reductions; in a few cases we obtain the Somos-4 and Somos-5 recurrences.

Keywords

Cite

@article{arxiv.2109.11107,
  title  = {Period 2 quivers and their T- and Y-systems},
  author = {Joe Pallister},
  journal= {arXiv preprint arXiv:2109.11107},
  year   = {2021}
}