Essential signatures and canonical bases of irreducible representations of the group G2 View Full Text


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Article Info

DATE

2015-01

AUTHORS

A. A. Gornitskii

ABSTRACT

We consider representations of simple Lie algebras and the problem of constructing a “canonical” weight basis in an arbitrary irreducible finite-dimensional highest-weight module. Vinberg suggested a method for constructing such bases by applying the lowering operators corresponding to all negative roots to the highest-weight vector and put forward a number of conjectures on the parametrization and structure of such bases. It follows from papers by Feigin, Fourier, and Littelmann that these conjectures are true for the cases of An and Cn. In the present paper, we prove these conjectures for the case of G2 by using a different approach suggested by Vinberg. More... »

PAGES

30-41

References to SciGraph publications

  • 2011-03. PBW filtration and bases for irreducible modules in type An in TRANSFORMATION GROUPS
  • 1998-06. Cones, crystals, and patterns in TRANSFORMATION GROUPS
  • Journal

    TITLE

    Mathematical Notes

    ISSUE

    1-2

    VOLUME

    97

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1134/s0001434615010046

    DOI

    http://dx.doi.org/10.1134/s0001434615010046

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1004826772


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