Miyawaki type lift for $GSpin(2,10)$

TL;DR

This paper constructs new holomorphic cusp forms on the Hermitian symmetric domain of $Spin(2,10)$ by extending previous work on forms related to $E_{7,3}$, inspired by Miyawaki lifts in symplectic groups.

Contribution

It introduces a Miyawaki-type lift for $GSpin(2,10)$, expanding the theory of automorphic forms on Hermitian symmetric domains.

Findings

Constructed holomorphic cusp forms on $rak T_2$ from elliptic cusp forms.

Extended the Miyawaki lift concept to the $GSpin(2,10)$ setting.

Established connections between forms on different Hermitian symmetric domains.

Abstract

Let $\frak T_2$ (resp. $\mathfrak{T}$) be the Hermitian symmetric domain of $Spin(2,10)$ (resp. $E_{7,3}$). In the previous work, we constructed holomorphic cusp forms on $\mathfrak{T}$ from elliptic cusp forms with respect to $SL_2(\mathbb{Z})$. By using such cusp forms we construct holomorphic cusp forms on $\mathfrak{T}_2$ which are similar to Miyawaki lift in symplectic groups established by T. Ikeda.