Comments on: Anders Bjoerner and Francesco Brenti, Affine permutations of type A

• at the end of section 3 (page 10) it is claimed that all maximal parabolic subgroups are isomorphic, and even conjugate. The first is true, the second is not (despite the fact that for $n>2$ all $n$ generators $s_i$ are individually conjugate).
• In equation (10), the variable $i$ should run over all integers, rather than the positive ones, in order to get obtain right value for negative $j$ (in particular to ensure that $\Inv_j(\sigma)=\Inv_{j+n}(\sigma)$ as claimed shortly after the equation).