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        Prime representations from a homological perspective

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        1112.6376v1_.pdf (PDF, 327Kb)
        Author
        Chari, Vyjayanthi
        Moura, Adriano
        Young, Charles A. S.
        Attention
        2299/10777
        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
        Publication date
        2013-06
        Published in
        Mathematische Zeitschrift
        Published version
        https://doi.org/10.1007/s00209-012-1088-7
        Other links
        http://hdl.handle.net/2299/10777
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