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On the Arakawa lifting Part I: Eichler commutation relations
- Part of
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- Journal:
- Nagoya Mathematical Journal / Volume 261 / 2026
- Published online by Cambridge University Press:
- 25 September 2026, e49
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We investigate the theta correspondence of cusp forms for the dual pair $(O^*(4),\mathrm {Sp}(1,1))$
originally introduced by Tsuneo Arakawa in the non-adelic setting. We call this Arakawa lifting. In this article, reformulating the theta correspondence in the adelic setting, we provide commutation relations of Hecke operators satisfied by the Arakawa lifting at all non-archimedean places, which is referred to as Eichler commutation relations for classical modular forms. Their archimedean analog is also given in terms of reproducing kernels.
