Projects per year
Abstract
We begin the study of simple finitedimensional prime representations of quantum affine algebras from a homological perspective. Namely, we explore the relation between self extensions of simple representations and the property of being prime. We show that every nontrivial simple module has a nontrivial self extension. Conversely, 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 language  English 

Number of pages  32 
Publication status  Published  Dec 2011 
Projects
 1 Finished

Nonultralocality and new mathematical structures in quantum integrability
MacKay, N., Regelskis, V., Sklyanin, E., Torrielli, A., Vicedo, B. & Young, C.
1/10/09 → 31/03/13
Project: Research project (funded) › Research