Growth of root multiplicities along imaginary root strings in Kac--Moody algebras

Lisa Carbone, Terence Coelho, Scott H. Murray +2

Let $\mathfrak{g}$ be a symmetrizable Kac--Moody algebra. Given a root $\alpha$ and a real root $\beta$ of $\mathfrak{g}$, it is known that the $\beta$-string through $\alpha$, denoted $R_{\alpha }(\beta )$, is…