English

Archimedean period relations for Rankin-Selberg convolutions

Representation Theory 2024-12-30 v1

Abstract

We formulate and prove the archimedean period relations for Rankin-Selberg convolutions of GL(n)×GL(n)\text{GL}(n)\times \text{GL}(n) and GL(n)×GL(n1)\text{GL}(n)\times \text{GL}(n-1), for all generic cohomological representations. As a consequence, we prove the non-vanishing of the archimedean modular symbols. This extends the earlier results in [LLS24] for essentially tempered representations of GL(n)×GL(n1)\text{GL}(n)\times\text{GL}(n-1).

Keywords

Cite

@article{arxiv.2412.18805,
  title  = {Archimedean period relations for Rankin-Selberg convolutions},
  author = {Yubo Jin and Dongwen Liu and Binyong Sun},
  journal= {arXiv preprint arXiv:2412.18805},
  year   = {2024}
}