Cohomology of Kac–Moody groups over a finite field

Abstract

We compute the mod p cohomology algebra of a family of infinite discrete Kac-Moody groups of rank two defined over finite fields of characteristic different from p.

Generalized invariants of reflection groups in rank two

“…As abstract groups, both U 2,1 and U 1,2 are isomorphic to the dihedral group of order 2p, but they are not conjugate. These groups are considered in [19] (pages 128-129), [16] and also in [3] and [2] where they appeared as mod p reductions of the (infinite) Weyl groups of some Kac-Moody groups.…”