On the unipotent characters of the Ree groups of type G₂

2008/07/23 by Olivier Brunat, Brunat, Olivier
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.0807.3766

arxiv created 2008/07/23 · arxiv updated 2009/12/01

Abstract

This note is concerned with the unipotent characters of the Ree groups of type G₂. We determine the roots of unity associated by Lusztig and Digne-Michel to unipotent characters of ²G₂(3²ⁿ⁺¹) and we prove that the Fourier matrix of ²G₂(3²ⁿ⁺¹) defined by Geck and Malle satisfies a conjecture of Digne-Michel. Our main tool is the Shintani descent of Ree groups of type G₂.

Related

• The Shintani descents of Suzuki Groups and consequences
• The values of unipotent characters at unipotent elements for groups of type E₈ and ² E₆
• Unipotent almost characters of simple p-adic groups, II
• Quadratic unipotent blocks in general linear, unitary and symplectic groups
• Character sheaves and generalizations