Characteristic polynomials and finitely dimensional representations of \mathfraksl(2, ℂ)

2021/12/15 by Tianyi Jiang, Jiang, Tianyi, Shoumin Liu +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2112.07933

openalex publication_date 2021/12/15 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we obtain a general formula for the characteristic polynomial of a finitely dimensional representation of Lie algebra \mathfraksl(2, \C ) and the form for these characteristic polynomials, and prove there is one to one correspondence between representations and their characteristic polynomials. We define a product on these characteristic polynomials, endowing them with a monoid structure.

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