This is an expanded version of the notes of my three lectures at a NATO Advanced Study Institute ``Symmetric functions 2001: surveys of developments and perspectives" (Isaac Newton Institute for Mathematical Sciences, Cambridge, UK; June 25-July 6, 2001). Lecture I presents a unified expression due to A. Berenstein and the author 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 introduced by S. Fomin and the author in an attempt to create an algebraic framework for canonical bases and total positivity.
CITATION STYLE
Zelevinsky, A. (2002). From Littlewood-Richardson Coefficients to Cluster Algebras in Three Lectures. In Symmetric Functions 2001: Surveys of Developments and Perspectives (pp. 253–273). Springer Netherlands. https://doi.org/10.1007/978-94-010-0524-1_7
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