Abstract
Lecture I presents a unified expression from [4] for generalized Littlewood- Richardson coefficients (= tensor product multiplicities) for any complex semisimple Lie algebra. Lecture II outlines a proof of this result; the main idea of the proof is to relate the LR-coefficients with canonical bases and total positivity. Lecture III introduces cluster algebras, a new class of commutative algebras defined in [9] in an attempt to create an algebraic framework for canonical bases and total positivity
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