Fueter-Regular Discete Series for Sp(1,1)
Zavosh Amir-Khosravi

TL;DR
This paper constructs a realization of quaternionic discrete series representations for Sp(1,1) using Fueter-regular functions and explores associated automorphic forms and their transformation properties.
Contribution
It introduces a novel realization of quaternionic discrete series via Fueter-regular functions and constructs a map to differential forms satisfying a cocycle condition.
Findings
Realization of quaternionic discrete series inside Fueter-regular functions.
Construction of automorphic forms with specific transformation properties.
Development of a map to closed differential forms satisfying cocycle conditions.
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 H^n. We then consider the corresponding -valued Fueter-regular automorphic forms on G. For a fixed level , we construct a non-trivial map from the space of pairs of such automorphic forms, to closed -valued differential -forms on , which transform under according to a cocycle condition.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Mathematical Analysis and Transform Methods · Holomorphic and Operator Theory
