## Abstract

Recently, a strong exponential character bound was established in [Acta Math. 221 (2018), pp. 1–57] for all elements g ∈ G^{F} of a finite reductive group G^{F} which satisfy the condition that the centralizer C_{G}(g) is contained in a (G,F)-split Levi subgroup M of G and that G is defined over a field of good characteristic. In this paper, assuming a weak version of Lusztig’s conjecture relating irreducible characters and characteristic functions of character sheaves holds, we considerably generalize this result by removing the condition that M is split. This assumption is known to hold whenever Z(G) is connected or when G is a special linear or symplectic group and G is defined over a sufficiently large finite field.

Original language | English (US) |
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Pages (from-to) | 8637-8676 |

Number of pages | 40 |

Journal | Transactions of the American Mathematical Society |

Volume | 373 |

Issue number | 12 |

DOIs | |

State | Published - Dec 2020 |

Externally published | Yes |

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics