AG Mathematische Physik, 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 $hin mathfrak{g}$ 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.