From Littlewood-Richardson Coefficients to Cluster Algebras in Three Lectures View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2002

AUTHORS

Andrei Zelevinsky

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 More... »

PAGES

253-273

References to SciGraph publications

  • 2001-01. Tensor product multiplicities, canonical bases and totally positive varieties in INVENTIONES MATHEMATICAE
  • 1997-05. Total positivity in Schubert varieties in COMMENTARII MATHEMATICI HELVETICI
  • 1993. Algorithms in Invariant Theory in NONE
  • 1994-12. A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras in INVENTIONES MATHEMATICAE
  • 1994. Total Positivity in Reductive Groups in LIE THEORY AND GEOMETRY
  • Book

    TITLE

    Symmetric Functions 2001: Surveys of Developments and Perspectives

    ISBN

    978-1-4020-0774-3
    978-94-010-0524-1

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-94-010-0524-1_7

    DOI

    http://dx.doi.org/10.1007/978-94-010-0524-1_7

    DIMENSIONS

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