Positively ratioed representations

Abstract

Let S be a closed orientable surface of genus at least 2 and let G be a semisimple real algebraic group of non-compact type. We consider a class of representations from the fundamental group of S to G 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.

59 pages, 10 figures, published version

References in corpus (3)

• A Morse Lemma for quasigeodesics in symmetric spaces and euclidean buildings
• Morse actions of discrete groups on symmetric space
• Maximal representations, non Archimedean Siegel spaces, and buildings

Cited by in corpus (1)

• A structure theorem for geodesic currents and length spectrum compactifications