def __init__(self, R, cartan_matrix, wt, prefix):
"""
Initialize ``self``.
"""
self._cartan_matrix = cartan_matrix
self._weight = wt
self._d = sum(wt)
# Reduced words
#red_words = Family(Permutations(self._d), lambda p: tuple(p.reduced_word()))
red_words = FiniteEnumeratedSet([tuple(p.reduced_word())
for p in Permutations(self._d)])
red_words.rename("reduced words of S_{}".format(self._d))
# The monomials
M = FreeAbelianMonoid(self._d, names=['x%s'%i for i in range(1, self._d+1)])
# Idempotents (i.e. the colors of the strands)
index_set = self._cartan_matrix.index_set()
P = Permutations(sum([[index_set[i]]*v for i,v in enumerate(wt)],[]))
I = cartesian_product([red_words, M, P])
CombinatorialFreeModule.__init__(self, R, I, prefix=prefix,
monomial_key=KLRAlgebra._monomial_key,
category=Algebras(R).WithBasis().Graded())
