Malle's degree-matching conjecture for cuspidal characters of finite Chevalley groups
Malle's degree-matching conjecture for cuspidal characters of finite Chevalley groups
Let be a power of the prime , let be a finite Chevalley group defined over with a bad prime for , and let be a Sylow -subgroup of . For a character degree , write for its -part. Malle's conjecture. For every cuspidal character , there exists such that
The conjecture predicts a strong connection between cuspidal character degrees of finite groups of Lie type and the degrees of irreducible characters of their Sylow -subgroups, supporting the use of induced characters from in studying modular representations and decomposition matrices. Its resolution status is not specified in the source.
Sources & referencesView supporting material
Primary source
Tung Le, Kay Magaard and Alessandro Paolini, “On the characters of Sylow p-subgroups of finite Chevalley groups G(p^f) for arbitrary primes”, arXiv:1904.00638 (2019).
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