  We give a new model for the crystal graphs of an affine Lie algebra g^,
combining Littelmann's path model with the Kyoto path model. The vertices of
the crystal graph are represented by certain infinitely looping paths which we
call skeins.
  We apply this model to the case when the corresponding finite-dimensional
algebra g has a minuscule representation (classical type and E_6, E_7). We
prove that the basic level-one representation of g^, when considered as a
representation of g, is an infinite tensor product of fundamental
representations of g. A similar tensor product phenomenon holds for certain
Demazure submodules of the basic representation.
