Uniform character bounds for finite classical groups

• 成果类型: Article
• 署名作者: Larsen, Michael; Tiep, Pham Huu
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2024.200.1.1
• 发表日期: 2024
• 页码: 1-70
• 关键词: conjugacy classes; symmetric-groups; irreducible representations; fuchsian-groups; sharp bounds; word maps; permutation; unitary; GROWTH

摘要

For every finite quasisimple group of Lie type G , every irreducible character chi of G , and every element g of G , we give an exponential upper bound for the character ratio chi ( g ) /chi (1) with exponent linear in log|G| | G | g G , or, equivalently, in the ratio of the support of g to the rank of G . We give several applications, including a proof of Thompson's conjecture for all sufficiently large simple symplectic groups, orthogonal groups in characteristic 2, and some other infinite families of orthogonal and unitary groups.