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arXiv · 1412.5549

Cusp forms for exceptional group of type $E_{7}$

Henry H. Kim·Takuya Yamauchi
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Abstract

Let $\bf{G}$ be the connected reductive group of type $E_{7,3}$ over $\mathbb{Q}$ and $\mathfrak{T}$ be the corresponding symmetric domain in $\mathbb{C}^{27}$. Let $Γ=\bf{G}(\mathbb{Z})$ be the arithmetic subgroup defined by Baily. In this paper, for any positive integer $k\ge 10$, we will construct a (non-zero) holomorphic cusp form on $\mathfrak{T}$ of weight $2k$ with respect to $Γ$ from a Hecke cusp form in $S_{2k-8}(SL_2(\mathbb{Z}))$. This lift is an analogue of Ikeda's construction.

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Henry H. Kim, Takuya Yamauchi. 2015-09-01. Cusp forms for exceptional group of type $E_{7}$. https://doi.org/10.1112/s0010437x15007538

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