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PreprintCC BY 4.0arXiv

Relative Langlands duality for linear periods

  • Tsao-Hsien Chen
  • Sanath K. Devalapurkar
  • Mark Macerato
  • David Nadler
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Abstract

We prove relative Langlands duality for X = GLp+q/(GLp × GLq). These symmetric spaces arise in the setting of the linear period of Friedberg-Jacquet when p=q, and exhibit non-tempered behavior when q>p+1. Via the real-symmetric correspondence, we establish a derived Satake equivalence for the real group Gℝ=U(p,q), and use it to obtain a constructible realization of coherent sheaves on Kato's exotic nilpotent cones. Along the way, we describe the dual variety of X in terms of the Whittaker cotangent bundle and regular centralizers, viewed as Coulomb branches.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026relative,
  title = {{Relative Langlands duality for linear periods}},
  author = {Tsao-Hsien Chen and Sanath K. Devalapurkar and Mark Macerato and David Nadler},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31771},
  eprint = {2610.31771},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31771},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Relative Langlands duality for linear periods
AU  - Tsao-Hsien Chen
AU  - Sanath K. Devalapurkar
AU  - Mark Macerato
AU  - David Nadler
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31771
UR  - https://arxiv.org/abs/2610.31771
AB  - We prove relative Langlands duality for X = GL_p+q/(GL_p × GL_q). These symmetric spaces arise in the setting of the linear period of Friedberg-Jacquet when p=q, and exhibit non-tempered behavior when q>p+1. Via the real-symmetric correspondence, we establish a derived Satake equivalence for the real group G_ℝ=U(p,q), and use it to obtain a constructible realization of coherent sheaves on Kato's exotic nilpotent cones. Along the way, we describe the dual variety of X in terms of the Whittaker cotangent bundle and regular centralizers, viewed as Coulomb branches.
ER  -