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PreprintCC BY 4.0arXiv

Exact Archimedean Flicker--Rallis Periods on Cohomological Minimal K-Types

  • Zheng Wang
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Abstract

For the symmetric pair (GLn(ℂ),GLn(ℝ)), we compute the exact Flicker--Rallis period of a distinguished vector in a cohomological minimal U(n)-type, normalized by the Gel'fand--Tsetlin pairing of Hara--Miyazaki--Namikawa. Our main tool is a weight-independent identity between the Whittaker period and a compact O(n)-average. We determine the proportionality constant using the archimedean newform formula of Humphries--Jo, and evaluate the compact functional on the normalized distinguished vector. This yields an explicit formula for the Flicker--Rallis period for every cohomological weight.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026exact,
  title = {{Exact Archimedean Flicker--Rallis Periods on Cohomological Minimal $K$-Types}},
  author = {Zheng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31018},
  eprint = {2610.31018},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31018},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Exact Archimedean Flicker--Rallis Periods on Cohomological Minimal K-Types
AU  - Zheng Wang
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31018
UR  - https://arxiv.org/abs/2610.31018
AB  - For the symmetric pair (GL_n(ℂ),GL_n(ℝ)), we compute the exact Flicker--Rallis period of a distinguished vector in a cohomological minimal U(n)-type, normalized by the Gel'fand--Tsetlin pairing of Hara--Miyazaki--Namikawa. Our main tool is a weight-independent identity between the Whittaker period and a compact O(n)-average. We determine the proportionality constant using the archimedean newform formula of Humphries--Jo, and evaluate the compact functional on the normalized distinguished vector. This yields an explicit formula for the Flicker--Rallis period for every cohomological weight.
ER  -