New supercharacter theory for Sylow subgroups in orthogonal and symplectic groups

TL;DR

This paper develops a new supercharacter theory for Sylow subgroups in orthogonal and symplectic groups over finite fields, leveraging embeddings of type A groups, resulting in more precise supercharacters.

Contribution

It introduces a novel supercharacter theory for Sylow subgroups in orthogonal and symplectic groups using embeddings from type A groups, improving precision over previous theories.

Findings

Supercharacters are more precise than earlier versions.

The theory applies to groups over finite fields.

Embedding techniques from type A groups are effective.

Abstract

Applying the embedding of $A_{n-1}$ in $B_n$, $C_n$ and $D_n$ we construct a new supercharacter theory for the Sylow subgroups in orthogonal and symplectic groups over a finite field. The constructed supercharacter appears to be a little bit more precise than the previously known one.