A Curtis–Tits–Phan theorem for the twin-building of type A˜n−1

The Curtis-Tits-Phan theory as laid out originally by Bennett and Shpectorov describes a way to employ Tits' lemma to obtain presentations of groups related to buildings as the universal completion of an amalgam of low-rank groups. It is formulated in terms of twin-buildings, but all concrete results so far were concerned with spherical buildings only. We describe an explicit flip-flop geometry for the twin-building of type (A) over tilde (n-1) associated to k vertical bar t, t(-1)vertical bar on which a unitary group SUn(k vertical bar t. t(-1)vertical bar, beta), related to a certain non-degenerate hermitian form beta, acts flag-transitively and obtain a presentation for this group in terms of a rank-2 amalgam consisting of unitary groups. This is the most natural generalization of the original result by Phan for the unitary groups. Published by Elsevier Inc.