English

Modular Solutions to Equations of Generalized Halphen Type

solv-int 2009-10-31 v3 High Energy Physics - Theory Mathematical Physics math.MP Quantum Algebra Exactly Solvable and Integrable Systems

Abstract

Solutions to a class of differential systems that generalize the Halphen system are determined in terms of automorphic functions whose groups are commensurable with the modular group. These functions all uniformize Riemann surfaces of genus zero and have qq--series with integral coefficients. Rational maps relating these functions are derived, implying subgroup relations between their automorphism groups, as well as symmetrization maps relating the associated differential systems.

Keywords

Cite

@article{arxiv.solv-int/9804006,
  title  = {Modular Solutions to Equations of Generalized Halphen Type},
  author = {J. Harnad and J. McKay},
  journal= {arXiv preprint arXiv:solv-int/9804006},
  year   = {2009}
}

Comments

PlainTeX 36gs. (Formula for Hecke operator corrected.)

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