Deforming Representations of SL(2,R)

2017/01/20 by Jeffrey Adams, Adams, Jeffrey
Mathematics · #17B10 #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.1701.05879

openalex publication_date 2017/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The spherical principal series representations π(ν) of SL(2,\mathbb R) is a family of infinite dimensional representations parametrized by ν∈\mathbb C. The representation π(ν) is irreducible unless ν is an odd integer, in which case it is indecomposable. We find a new continuous family of representations Π(ν) such that π(ν) and Π(ν) have the same composition factors, and Π(ν) is completely reducible, for all ν. We also describe a connection between this construction and families of invariant Hermitian forms on the representations.

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