  We give an explicit Baxterisation formula for the fused Hecke algebra and its
classical limit for the algebra of fused permutations. These algebras replace
the Hecke algebra and the symmetric group in the Schur--Weyl duality theorems
for the symmetrised powers of the fundamental representation of gl(N) and their
quantum version. So the Baxterisation formulas presented in this paper are
applicable to the $R$-matrices associated to these representations. In
particular all "higher spins" representations of (classical and quantum) sl(2)
are covered.
