  Using the tensor product variety introduced by Malkin and Nakajima, the
complete structure of the tensor product of a finite number of integrable
highest weight modules of U_q(sl_2) is recovered. In particular, the elementary
basis, Lusztig's canonical basis, and the basis adapted to the decomposition of
the tensor product into simple modules are all exhibited as distiguished
elements of certain spaces of invariant functions on the tensor product
variety. For the latter two bases, these distinguished elements are closely
related to the irreducible components of the tensor product variety. The space
of intertwiners is also interpreted geometrically.
