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Abstract view

# Integral Representation for $U_{3} \times \GL_{2}$

Gelbart and Piatetskii-Shapiro constructed various integral representations of Rankin--Sel\-berg type for groups $G \times \GL_{n}$, where $G$ is of split rank $n$. Here we show that their method can equally well be applied to the product $U_{3} \times \GL_{2}$, where $U_{3}$ denotes the quasisplit unitary group in three variables. As an application, we describe which cuspidal automorphic representations of $U_{3}$ occur in the Siegel induced residual spectrum of the quasisplit $U_{4}$.
 MSC Classifications: 11F70 - Representation-theoretic methods; automorphic representations over local and global fields 11F67 - Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols