On irreducible (B,N)-pairs of rank 2

Let G be a group with an irreducible spherical (B,N)-pair of rank 2 where B has a normal subgroup U with B = UT for T = B boolean AND N. Let B be the generalized n-gon associated to this (B,N)-pair and let W be the associated Weyl group. So T stabilizes an ordinary n-gon in B, and \W \ = 2n. We prov e that, if either U is nilpotent or G acts effectively on B and Z(U) not eq ual 1, then \W \ = 2n with n = 3, 4, 6, 8 or 12. If G acts effectively and n not equal 4, 6, then (up to duality) Z(U) consists of central elations. A lso, if n = 3 and U is nilpotent, then B is a Moufang projective plane and if, moreover, G acts effectively on B, then it contains its little projecti ve group. Finally, we show that, if G acts effectively on B, if Z(U) not eq ual 1, and if T satisfies a certain strong transitivity assumption, then B is a Moufang n-gon with n = 3, 4 or 6 and G contains its little projective group.