On q, t-characters and the l-weight Jordan Filtration of Standard Uq(Ŝl2)-modules

Charles A. S. Young, Robin Zegers

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    Abstract

    The Cartan subalgebra of the sl2 quantum affine algebra is generated by a family of mutually commuting operators, responsible for the l-weight decomposition of finite dimensional modules. The natural Jordan filtration induced by these operators is generically non-trivial on l-weight spaces of dimension greater than one. We derive, for every standard module of quantum affine sl2, the dimensions of the Jordan grades and prove that they can be directly read off from the t-dependence of the q,t-characters introduced by Nakajima. To do so we construct explicit bases for the standard modules with respect to which the Cartan generators are upper-triangular. The basis vectors of each l-weight space are labelled by the elements of a ranked poset from the family L(m,n)
    Original languageEnglish
    Pages (from-to)2179-2211
    JournalInternational Mathematical Research Notices
    Volume2012
    Issue number10
    Early online date8 Jun 2011
    DOIs
    Publication statusPublished - 2012

    Keywords

    • math.QA
    • 2010: Primary 17B37, Secondary 81R50

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