Positively ratioed representations

  • Giuseppe Martone

    University of Michigan, Ann Arbor, USA
  • Tengren Zhang

    National University of Singapore, Singapore
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Abstract

Let be a closed orientable surface of genus at least 2 and let be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of to called positively ratioed representations. These are Anosov representations with the additional condition that certain associated cross ratios satisfy a positivity property. Examples of such representations include Hitchin representations and maximal representations. Using geodesic currents, we show that the corresponding length functions for these positively ratioed representations are well-behaved. In particular, we prove a systolic inequality that holds for all such positively ratioed representations.

Cite this article

Giuseppe Martone, Tengren Zhang, Positively ratioed representations. Comment. Math. Helv. 94 (2019), no. 2, pp. 273–345

DOI 10.4171/CMH/461