Canonical bases in tensor products.
I construct a canonical basis in the tensor product of a simple integrable highest weight module with a simple integrable lowest weight module of a quantized enveloping algebra. This basis is simultaneously compatible with many submodules of the tensor product. As an application, I obtain a construction of a canonical basis of (a modified form of) the quantized enveloping algebra.
Lusztig
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Department of Mathematics, Massachusetts Institute of Technology, Cambridage, MA 02139, USA.