Positivity and higher Teichm\"uller theory

By Olivier Y Guichard, Anna Wienhard. 2018

58 citations recorded by the source corpus.

We introduce $\Theta$-positivity, a new notion of positivity in real semisimple Lie groups. The notion of $\Theta$-positivity generalizes at the same time Lusztig's total positivity in split real Lie groups as well as well known concepts of positivity in Lie groups of Hermitian type. We show that there are two other families of Lie groups, SO(p,q) for p<q, and a family of exceptional Lie groups, which admit a $\Theta$-positive structure. We describe key aspects of $\Theta$-positivity and make a connection with representations of surface groups and higher Teichmuller theory.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c7ee00951d2231a557e039ef483545f3d301785b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Nicolas Tholozan
2. J'er'emy Toulisse
3. Brian Collier
4. Anna Wienhard

In Mathematical Physics

1. Nicolas Tholozan
2. J'er'emy Toulisse
3. Brian Collier
4. Anna Wienhard

Citations in the corpus

• The geometry of maximal representations of surface groups into SO0(2,n) (2017, background): “There have been several attempts to propose a unifying characterization of these representations (see [MZ16] and [GW16]).”