Let us consider $GL_n(K)$ over a local field $K$. It has standard subgroups $N$ and $B$. $B$ is Iwahori subgroup, $N$ consists of monomial matrices. The pair comes close to a romantic ending, i.e. forming a BN-pair, as one gets a building of affine type out of it. However, it fails axiom (BN2) asking $sBs^{-1}\not = B$. You can also observe other things are out of order: maximal parabolics of different type are conjugate, etc...

**What is the set of axioms governing this generalized BN-pair that alows all the usual building geometry to take place? Is there a name and other meaningful examples?**

Please, help, I cannot sleep all day because it bothers me greatly.