Prime representations from a homological perspective

Vyjayanthi Chari, Adriano Moura, Charles A. S. Young

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    11 Citations (Scopus)
    98 Downloads (Pure)

    Abstract

    We explore the relation between self extensions of simple representations of quantum affine algebras and the property of a simple representation being prime. We show that every nontrivial simple representation has a nontrivial self extension. Conversely, we prove that if a simple representation has a unique nontrivial self extension up to isomorphism, then its Drinfeld polynomial is a power of the Drinfeld polynomial of a prime representation. It turns out that, in the sl 2 -case, a simple module is prime if and only if it has a unique nontrivial self extension up to isomorphism. It is tempting to conjecture that this is true in general and we present a large class of prime representations satisfying this homological property
    Original languageEnglish
    Pages (from-to)613-645
    JournalMathematische Zeitschrift
    Volume274
    Issue number1-2
    Early online date8 Nov 2012
    DOIs
    Publication statusPublished - Jun 2013

    Keywords

    • Quantum Affine Algebras
    • Extensions
    • Prime

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