Elliptic points of the Drinfeld modular groups

Abstract

Let be an algebraic function field with constant field . Fix a place of of degree and let be the ring of elements of that are integral outside . We give an explicit description of the elliptic points for the action of the Drinfeld modular group on the Drinfeld's upper half-plane and on the Drinfeld modular curve . It is known that under the building map elliptic points are mapped onto vertices of the Bruhat-Tits tree of . We show how such vertices can be determined by a simple condition on their stabilizers. Finally for the special case we obtain from this a surprising free product decomposition for.