Extremal loop weight modules and tensor products for quantum toroidal algebras
Abstract
We define integrable representations of quantum toroidal algebras of type A by tensor product, using the Drinfeld "coproduct". This allow us to recover the vector representations recently introduced by FeiginJimboMiwaMukhin [6] and constructed by the author [21] as a subfamily of extremal loop weight modules. In addition we get new extremal loop weight modules as subquotients of tensor powers of vector representations. As an application we obtain finitedimensional representations of quantum toroidal algebras by specializing the quantum parameter at roots of unity.
 Publication:

arXiv eprints
 Pub Date:
 May 2013
 arXiv:
 arXiv:1305.3481
 Bibcode:
 2013arXiv1305.3481M
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Representation Theory
 EPrint:
 30 pages