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arXiv · 1305.3481

Extremal loop weight modules and tensor products for quantum toroidal algebras

Mathieu Mansuy
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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 Feigin-Jimbo-Miwa-Mukhin [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 finite-dimensional representations of quantum toroidal algebras by specializing the quantum parameter at roots of unity.

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Mathieu Mansuy. 2015-01-23. Extremal loop weight modules and tensor products for quantum toroidal algebras. https://arxiv.org/abs/1305.3481

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