arXiv subjects
Publications and source records attributed to Nozomi Ito.
Double descent is a method to construct automorphic representations of classical groups. For given A-parameter $ψ$ with certain good properties, double descent constructs a space of functions orthogonal to any cuspidal representation whose A-parameter is not $ψ$ and not orthogonal to any cuspidal representation with A-parameter $ψ$. In this paper, we show that functions constructed by double descent are always square-integrable.
The Miyawaki lifting is a lifting of Siegel modular forms introduced by Ikeda in his 2006 paper. In the same paper, he also conjectured a formula for the norms of Miyawaki lifts. In this paper, we show that his conjectural formula can be rewritten into a refined GGP type formula.
In this paper, we consider the branching law of the Speh representation $\mathrm{Sp}(π,n+l)$ of $\mathrm{GL}_{2n+2l}$ with respect to the block diagonal subgroup $\mathrm{GL}_n\times\mathrm{GL}_{n+2l}$ for any irreducible generic representation $π$ of $\mathrm{GL}_2$ over any $p$-adic field. We use the Shalika model of $\mathrm{Sp}(π,n)$ to construct certain zeta integrals, which were defined by Ginzburg and Kaplan independently, and study them. Finally, using these zeta integrals, we obtain a nonzero $\mathrm{GL}_n\times\mathrm{GL}_{n+2l}$-map from $\mathrm{Sp}(π,n+l)$ to $τ\boxtimesτ^\veeχ_π\times\mathrm{Sp}(π, l)$ for any irreducible representation $τ$ of $\mathrm{GL}_n$. These results form part of the local theory of the Miyawaki lifting for unitary groups.
In this paper, we discuss the representation-theoretical Miyawaki lift for unitary groups in terms of the endoscopic classification. We give an explicit determination of Miyawaki lifts for U(1) and U(3) with respect to Hermitian Maass lifts, namely Ikeda lifts for U(4).