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A Note on Nahm's Conjecture in Rank 2 Case

Mathematical Physics 2011-06-06 v3 High Energy Physics - Theory Algebraic Geometry math.MP Number Theory

Abstract

The aim of this paper is to get a complete list of positive definite symmetric matrices with integer entries \a&b\b&d\ such that all complex solutions to the system of equations 1x1=x1ax2b 1x2=x1bx2d1-x_1=x_1^ax_2^b\ 1-x_2=x_1^bx_2^d are real. This result is related to Nahm's conjecture in rank 2 case.

Cite

@article{arxiv.1008.4981,
  title  = {A Note on Nahm's Conjecture in Rank 2 Case},
  author = {An Huang and Chul-hee Lee},
  journal= {arXiv preprint arXiv:1008.4981},
  year   = {2011}
}

Comments

14 pages. Submitted Version

R2 v1 2026-06-21T16:06:35.977Z