Root strings with two consecutive real roots (Q1902883)

Let \({\mathfrak g}\) be a Kac-Moody Lie algebra. The authors call an unordered pair of positive real roots \(\{\alpha, \beta\}\) to be a Morita pair if \(\alpha- \beta\) is not a root, \(\alpha+ \beta\) is a real root and \(\text{ht} (\alpha+ \beta)\leq \text{ht} (w (\alpha+ \beta))\) for all the Weyl group elements \(w\). The aim of the paper under review is to study the Morita pairs (following the study of such pairs by J. Morita). The main result completely classifies such pairs.