|Dept.||The University of Connecticut|
Eisenstein series play an important role in the theory of automorphic forms on reductive groups. On the other hand, Kac-Moody groups are infinite dimensional groups, and only recently there have been attempts to define Eisenstein series and automorphic forms on Kac--Moody groups which found applications in string theory in physics.
In this talk, we consider Eisenstein series on an arbitrary Kac–Moody group, induced from quasi-characters, and prove the almost-everywhere convergence of Kac--Moody Eisenstein series inside the Tits cone for spectral parameters in the Godement range. For a certain class of Kac-Moody groups satisfying an additional combinatorial property, we show absolute convergence everywhere in the Tits cone for spectral parameters in the Godement range. This is a joint work with Carbone, Garland, Miller and Liu.