AG Mathematische Physik, Tim Rotheneder (FAU): Positivity Domains and Coverings of Compactly Causal Symmetric Spaces

Tim Rotheneder (FAU)

Positivity Domains and Coverings of Compactly Causal Symmetric Spaces

Abstract:

Given a compactly causal symmetric Lie algebra $(\mathfrak{g},\tau,C)$ and

an Euler element $h\in \mathfrak{g}$ as infinitesimal data and an

associated causal symmetric space $(G,H,\tau,C)$ with $M:= G/H$, we discuss

how the topology of the positivity region $W_M^+(h)$ depends on the global

choice of $G$ and $H$. Eventually, we apply our theoretical results to the

anti-de Sitter example, i.e. $\mathfrak{g} = \mathfrak{so}_{2,d}(\R)$,

$\tau$ is conjugation with $I_{1,d+1}$ and $C$ is the forward light cone.