Fueter-Regular Discete Series for Sp(1,1)

2019/12/09 by Zavosh Amir-Khosravi, Amir-Khosravi, Zavosh
Mathematics · #11Fxx #22E46 #Algebraic and Geometric Analysis #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1912.04178

openalex publication_date 2019/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the quaternionic discrete series on G=Sp(1,1) with minimal K-type of dimension n+1 can be realized inside the space of Fueter-regular functions on the quaternionic ball B in H, with values in Hⁿ. We then consider the corresponding Hⁿ-valued Fueter-regular automorphic forms on G. For a fixed level Γ, we construct a non-trivial map from the space of pairs of such automorphic forms, to closed M_n(H)-valued differential 3-forms on B, which transform under Γ according to a cocycle condition.

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