Quantum groups, q-Boson algebras and quantized Weyl algebras

preprint2010arXivOpen access

Abstract

We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category O(Bq)\mathcal{O}(B_q) introduced by T.Nakashima and the classification of all simple objects in it.

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