  In our previous paper math.QA/0409261, we defined a deformation of the group
algebra of the group of even elements of a Coxeter group W, and showed that it
is flat for all values of parameters if and only if all the rank 3 parabolic
subgroups of W are infinite. In this paper, we study what happens in the
general case. Then the deformation is flat only for some values of parameters,
and the set of all such values is called the flatness locus. The main result of
the paper is an explicit description of the this flatness locus as a scheme
over Z. More specifically, we show that this scheme is the intersection of the
flatness loci for the subalgebras corresponding to parabolic subgroups of rank
3. The latter are determined by solving the rigid multiplicative
Deligne-Simpson problem. We also define additive analogs of our algebras and
study their properties.
