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PreprintCC BY-SA 4.0arXiv

Jacquet--Rallis transfer for GL(2)

  • Andreas Mihatsch
  • Siddarth Sankaran
  • Tonghai Yang
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Abstract

We study archimedean smooth transfer for the Jacquet--Rallis relative trace formula comparison, in particular, identities between orbital integrals on GL(n) and its unitary forms. We work with Lie algebras and a (g,K)-module setting. Our main result states that for n=2, meaning GL(2) acting on gl(3), every polynomial type Schwartz function has a transfer to the unitary side and vice versa. Our proof relies on the Weil representation and the study of invariant differential operators. It also suggests certain structural properties of the (g,K)-modules in question which we formulate as conjectures.

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Cite

BibTeXRIS
BibTeX
@misc{mihatsch2026jacquetrallis,
  title = {{Jacquet--Rallis transfer for GL(2)}},
  author = {Andreas Mihatsch and Siddarth Sankaran and Tonghai Yang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.13119},
  eprint = {2609.13119},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.13119},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Jacquet--Rallis transfer for GL(2)
AU  - Andreas Mihatsch
AU  - Siddarth Sankaran
AU  - Tonghai Yang
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.13119
UR  - https://arxiv.org/abs/2609.13119
AB  - We study archimedean smooth transfer for the Jacquet--Rallis relative trace formula comparison, in particular, identities between orbital integrals on GL(n) and its unitary forms. We work with Lie algebras and a (g,K)-module setting. Our main result states that for n=2, meaning GL(2) acting on gl(3), every polynomial type Schwartz function has a transfer to the unitary side and vice versa. Our proof relies on the Weil representation and the study of invariant differential operators. It also suggests certain structural properties of the (g,K)-modules in question which we formulate as conjectures.
ER  -