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The Tensor Product of Representations of U_q(sl_2) Via Quivers

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.