The triality of the twisted discrete trace formula for PGSO(8)
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866912974201946112 |
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| author | Du, Tuoping Pen, Zhifeng Wan, Haoyang |
| author_facet | Du, Tuoping Pen, Zhifeng Wan, Haoyang |
| contents | In this paper, we establish the triality twisted trace formula for PGSO(8), including its discrete part, and obtain a coarse classification of its automorphic representations by combining the properties of triality. By comparing the standard trace formula for G_2 with the triality twisted trace formula for PGSO(8), we derive a corresponding coarse classification for automorphic representations of G_2. Specifically, we construct the triality-twisted elliptic endoscopic data for PGSO(8), and the elliptic endoscopic data for G_2. Based on these constructions and the general framework of trace formulas, we establish the relevant trace formulas. Utilizing the triality property of PGSO(8), we obtain a coarse classification of its automorphic representations, which in turn yields a coarse classification for those of G_2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18763 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The triality of the twisted discrete trace formula for PGSO(8) Du, Tuoping Pen, Zhifeng Wan, Haoyang Number Theory In this paper, we establish the triality twisted trace formula for PGSO(8), including its discrete part, and obtain a coarse classification of its automorphic representations by combining the properties of triality. By comparing the standard trace formula for G_2 with the triality twisted trace formula for PGSO(8), we derive a corresponding coarse classification for automorphic representations of G_2. Specifically, we construct the triality-twisted elliptic endoscopic data for PGSO(8), and the elliptic endoscopic data for G_2. Based on these constructions and the general framework of trace formulas, we establish the relevant trace formulas. Utilizing the triality property of PGSO(8), we obtain a coarse classification of its automorphic representations, which in turn yields a coarse classification for those of G_2. |
| title | The triality of the twisted discrete trace formula for PGSO(8) |
| topic | Number Theory |
| url | https://arxiv.org/abs/2603.18763 |