A multiparameter family of irreducible representations of the quantum\n plane and of the quantum Weyl algebra

2014/07/24 by Samuel A. Lopes, Lopes, Samuel A., João Lourenço +1
Mathematics · #16S85 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 16D60 #Representation Theory (math.RT) #Secondary 16S80

paper · pdf · doi:10.48550/arxiv.1407.6646

openalex publication_date 2014/07/24 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We construct a family of irreducible representations of the quantum plane and\nof the quantum Weyl algebra over an arbitrary field, assuming the deformation\nparameter is not a root of unity. We determine when two representations in this\nfamily are isomorphic, and when they are weight representations, in the sense\nof Bavula.\n

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