PreprintCC BY 4.0arXiv
Even-degree Hermitian Ikeda lifts via Fourier-Jacobi descent
Abstract
Let E/F be a CM extension and let m≥2 be an even integer. Starting from the odd-degree Hermitian Ikeda lift of degree m+1 constructed by Yamana, we construct a Hermitian Ikeda lift of degree m from the theta components of its first Fourier-Jacobi coefficient. We determine its global Arthur parameter and its local constituents at every finite place. Using the global multiplicity formula for unitary groups, we obtain an explicit multiplicity-free decomposition of the resulting representation of Um.m(𝔸F,h) and show that its isomorphism class is independent of the Fourier-Jacobi index. When F=ℚ, we compare Fourier coefficients and identify the construction with Ikeda's even-degree Hermitian lift.
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BibTeX
@misc{takeda2026evendegree,
title = {{Even-degree Hermitian Ikeda lifts via Fourier-Jacobi descent}},
author = {Nobuki Takeda},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17396},
eprint = {2609.17396},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17396},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Even-degree Hermitian Ikeda lifts via Fourier-Jacobi descent
AU - Nobuki Takeda
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17396
UR - https://arxiv.org/abs/2609.17396
AB - Let E/F be a CM extension and let m≥2 be an even integer. Starting from the odd-degree Hermitian Ikeda lift of degree m+1 constructed by Yamana, we construct a Hermitian Ikeda lift of degree m from the theta components of its first Fourier-Jacobi coefficient. We determine its global Arthur parameter and its local constituents at every finite place. Using the global multiplicity formula for unitary groups, we obtain an explicit multiplicity-free decomposition of the resulting representation of U_m.m(𝔸_F,h) and show that its isomorphism class is independent of the Fourier-Jacobi index. When F=ℚ, we compare Fourier coefficients and identify the construction with Ikeda's even-degree Hermitian lift.
ER -