Supercharacters of the Sylow p-subgroups of the finite symplectic and orthogonal groups

2008/04/27 by Carlos A. M. André, André, Carlos A. M., Ana Margarida Neto +1
Computer Science · Engineering · Mathematics · #20C15 #20G40 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0804.4285

openalex publication_date 2008/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

We define and study supercharacters of the classical finite unipotent groups of symplectic and orthogonal types (over any finite field of odd characteristic). We show how supercharacters for groups of those types can be obtained by restricting the supercharacter theory of the finite unitriangular group, and prove that supercharacters are orthogonal and provide a partition of the set of all irreducible characters. We also describe all irreducible characters of maximum degree in terms of the root system, and show how they can be obtained as constituents of particular supercharacters.

Related

• A supercharacter theory for the Sylow p-subgroups of the finite symplectic and orthogonal groups
• New supercharacter theory for Sylow subgroups in orthogonal and symplectic groups
• Supercharacters of unipotent and solvable groups
• Supercharacter theories for Sylow p-subgroups of Lie type G₂
• supercharacter table of certain finite groups