Characters of the Borel and Sylow subgroups of classical groups

✍ Scribed by Balázs Szegedy

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 86 KB
• Volume: 267
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00344-2

✦ Synopsis

Let G be a classical group over the field with q = p d elements. We prove that if p is an odd prime then the irreducible characters of the Sylow p-subgroup of G have degrees that are powers of q. Moreover, we prove that if p is odd and G is not the unitary group then the Borel subgroup of G is an M-group and its character degrees as well as the sizes of the conjugacy classes can be written in the form q r (q -1) s 2 k .