Geometric and Unipotent Crystals View Full Text


Ontology type: schema:Chapter      Open Access: True


Chapter Info

DATE

2010

AUTHORS

Arkady Berenstein , David Kazhdan

ABSTRACT

Let G be a split semisimple algebraic group over ℚ, g be the Lie algebra of G and Uq(g) be the corresponding quantized enveloping algebra. Lusztig has introduced in [Lul] canonical bases for finite-dimensional Uq(g)-modules. About the same time E as hi war a introduced in [Kl] crystal bases as a natural framework for parametrizing bases of finite-dimensional Uq(g)-modules. It was shown in [Lu2] that Eashiwara’s crystal bases are the limits as q → 0 of Lusztig’s canonical bases. Later, in [K2] Kashiwara introduced a new combinatorial concept — crystals. Kashiwara’s crystals generalize the crystal bases and provide a natural framework for their study. More... »

PAGES

188-236

References to SciGraph publications

  • 1994-12. A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras in INVENTIONES MATHEMATICAE
  • 1997-05. Total positivity in Schubert varieties in COMMENTARII MATHEMATICI HELVETICI
  • 1990-10. Crystalizing theq-analogue of universal enveloping algebras in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1992. Introduction to Quantized Enveloping Algebras in NEW DEVELOPMENTS IN LIE THEORY AND THEIR APPLICATIONS
  • Book

    TITLE

    Visions in Mathematics

    ISBN

    978-3-0346-0421-5
    978-3-0346-0422-2

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-0346-0422-2_8

    DOI

    http://dx.doi.org/10.1007/978-3-0346-0422-2_8

    DIMENSIONS

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