Geometric Reflections and Cayley Graph-Reflections (Type A1)

In this work, we consider geometric reflections based on elements of a reflectable base of an extended affine root system R, and prove that in type A1, any geometric reflection of a reflectable base is a Cayley graph- reflection if and only if the nullity of R is less than or equal one. Also we show that any extended affine root system R, is a union of extended affine root systems of type A1 with the same nullities as the nullity of R.