Irreducibility of Theta Lifting for Unitary Groups
Chenyan Wu
TL;DR
This paper proves that the first theta lift of an irreducible cuspidal automorphic representation for unitary dual reductive pairs is irreducible, and establishes key properties of theta lifts such as tower and involutive properties.
Contribution
It introduces new irreducibility results and refined properties of theta lifts for unitary groups, advancing understanding of automorphic representation theory.
Findings
First occurrence of theta lift is irreducible for unitary dual pairs
Proves a refined tower property for theta lifts
Establishes involutive property for twisted theta lifts
Abstract
This article shows that for unitary dual reductive pairs the first occurrence of theta lift of an irreducible cuspidal automorphic representation is irreducible. It also proves a refined tower property for theta lifts and the involutive property for twisted theta lifts.
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