From Littlewood-Richardson coefficients to cluster algebras in three lectures
Abstract
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.
Keywords
Cite
@article{arxiv.math/0112062,
title = {From Littlewood-Richardson coefficients to cluster algebras in three lectures},
author = {Andrei Zelevinsky},
journal= {arXiv preprint arXiv:math/0112062},
year = {2007}
}
Comments
Latex, 17 pages, Theorem 3.2 corrected