A Family of GLr Multiplicative Higgs Bundles on Rational Base

  title={A Family of GLr Multiplicative Higgs Bundles on Rational Base},
  author={Rouven Frassek and Vasily Pestun},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  • Rouven Frassek, V. Pestun
  • Published 2 August 2018
  • Physics, Mathematics
  • Symmetry, Integrability and Geometry: Methods and Applications
In this paper we study a restricted family of holomorphic symplectic leaves in the Poisson-Lie group ${\rm GL}_r(\mathcal{K}_{\mathbb{P}^1_x})$ with rational quadratic Sklyanin brackets induced by a one-form with a single quadratic pole at $\infty \in \mathbb{P}_{1}$. The restriction of the family is that the matrix elements in the defining representation are linear functions of $x$. We study how the symplectic leaves in this family are obtained by the fusion of certain fundamental symplectic… Expand

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