Finite-dimensional irreducible modules of the racah algebra at characteristic zero

Hau Wen Huang, Sarah Bockting-Conrad

研究成果: 雜誌貢獻期刊論文同行評審

11 引文 斯高帕斯(Scopus)

摘要

Assume that F is an algebraically closed field with characteristic zero. The Racah algebra ℜ is the unital associative F-algebra defined by generators and relations in the following way. The generators are A, B, C, D and the relations assert that [A, B] = [B, C] = [C, A] = 2D and that each of [A, D]+AC−BA, [B, D]+BA−CB, [C, D]+CB−AC is central in ℜ. In this paper we discuss the finite-dimensional irreducible R-modules in detail and classify them up to isomorphism. To do this, we apply an infinite-dimensional R-module and its universal property. We additionally give the necessary and sufficient conditions for A, B, C to be diagonalizable on finite-dimensional irreducible R-modules.

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文章編號018
期刊Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
16
DOIs
出版狀態已出版 - 2020

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