  Soergel's category B_k(V) over a field k is defined from a Coxeter system
(W,S) and a k-linear representation V of W. It's a categorification of the
Hecke algebra of (W,S). In this article we prove that for some representations
V and V' of W, Soergel's conjecture over B_k(V') is equivalent to that over
B_k(V). In particular, when k=IR we can choose V' to be the geometric
representation.
