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PreprintCC BY 4.0arXiv

Loop spaces, twistor ℙ1 and tempiric parameters

  • Tsao-Hsien Chen
  • Lingfei Yi
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Abstract

We establish bijections among spherical orbits on loop symmetric spaces, principal bundles on the twistor ℙ1, and tempiric Langlands parameters. Using Vogan's theory of minimal K-types, we further establish bijections among irreducible equivariant local systems on loop symmetric spaces, irreducible local systems on principal bundles on the twistor ℙ1, and irreducible representations of all strong inner forms of the dual symmetric subgroup. The latter bijections may be viewed as a combinatorial shadow of geometric Langlands duality for real reductive groups.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026loop,
  title = {{Loop spaces, twistor $\mathbb P^1$ and tempiric parameters}},
  author = {Tsao-Hsien Chen and Lingfei Yi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16246},
  eprint = {2609.16246},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16246},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Loop spaces, twistor ℙ^1 and tempiric parameters
AU  - Tsao-Hsien Chen
AU  - Lingfei Yi
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.16246
UR  - https://arxiv.org/abs/2609.16246
AB  - We establish bijections among spherical orbits on loop symmetric spaces, principal bundles on the twistor ℙ^1, and tempiric Langlands parameters. Using Vogan's theory of minimal K-types, we further establish bijections among irreducible equivariant local systems on loop symmetric spaces, irreducible local systems on principal bundles on the twistor ℙ^1, and irreducible representations of all strong inner forms of the dual symmetric subgroup. The latter bijections may be viewed as a combinatorial shadow of geometric Langlands duality for real reductive groups.
ER  -