The Picky Conjecture for groups of Lie type
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912662702522368 |
|---|---|
| author | Malle, Gunter Fry, A. A. Schaeffer |
| author_facet | Malle, Gunter Fry, A. A. Schaeffer |
| contents | Recently, Moretó and Rizo proposed a conjecture, known as the Picky Conjecture, proposing new character correspondences extending the McKay Conjecture. We prove the Picky Conjecture for all quasi-simple groups of Lie type for non-defining primes. In favourable situations, we also obtain the stronger version postulating preservation of character values up to sign, and we show this stronger version holds in general when assuming certain natural properties of Lusztig's Jordan decomposition. Along the way, we complete the determination of semisimple picky elements in these groups by classifying picky 2- and 3-elements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18397 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Picky Conjecture for groups of Lie type Malle, Gunter Fry, A. A. Schaeffer Representation Theory 20C15, 20C33, 20D20, 20E25 Recently, Moretó and Rizo proposed a conjecture, known as the Picky Conjecture, proposing new character correspondences extending the McKay Conjecture. We prove the Picky Conjecture for all quasi-simple groups of Lie type for non-defining primes. In favourable situations, we also obtain the stronger version postulating preservation of character values up to sign, and we show this stronger version holds in general when assuming certain natural properties of Lusztig's Jordan decomposition. Along the way, we complete the determination of semisimple picky elements in these groups by classifying picky 2- and 3-elements. |
| title | The Picky Conjecture for groups of Lie type |
| topic | Representation Theory 20C15, 20C33, 20D20, 20E25 |
| url | https://arxiv.org/abs/2510.18397 |