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arXiv · 1907.06229

Finite dimensional modules over quantum toroidal algebras

Limeng Xia
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Abstract

The representations of the quantum toroidal algebras have been widely studied by many authors. However, no one has constructed some finite dimensional modules for them while $q$ is generic. In this paper, for all $\mathfrak{g}$-generic $q$, if $\mathfrak{g}$ is not of type $A_1$, we prove that the quantum toroidal algebra $U_q(\mathfrak{g}_{\rm tor})$ has no nontrivial finite dimensional simple module.

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BibTeXRIS

Limeng Xia. 2020-03-15. Finite dimensional modules over quantum toroidal algebras. https://arxiv.org/abs/1907.06229

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