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.
References
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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