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On the Hiraga-Ichino-Ikeda conjecture on formal degrees for G2

  • Yugo Takanashi
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Abstract

We prove that the twisted endoscopic character identities between triality PGSO8 and the endoscopic group G2 imply the Hiraga-Ichino-Ikeda conjecture on formal degrees for G2. In the course of proving the main result, we also establish some fundamental results on representation theory of PGSO8 with triality. A key feature of our approach is an application of the adjoint group of type E6.

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Cite

BibTeXRIS
BibTeX
@misc{takanashi2026hiragaichinoikeda,
  title = {{On the Hiraga-Ichino-Ikeda conjecture on formal degrees for $\mathrmG_2$}},
  author = {Yugo Takanashi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.19430},
  eprint = {2609.19430},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.19430},
}
RIS
TY  - UNPB
TI  - On the Hiraga-Ichino-Ikeda conjecture on formal degrees for G_2
AU  - Yugo Takanashi
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.19430
UR  - https://arxiv.org/abs/2609.19430
AB  - We prove that the twisted endoscopic character identities between triality PGSO_8 and the endoscopic group G_2 imply the Hiraga-Ichino-Ikeda conjecture on formal degrees for G_2. In the course of proving the main result, we also establish some fundamental results on representation theory of PGSO_8 with triality. A key feature of our approach is an application of the adjoint group of type E_6.
ER  -