Supercharacters for parabolic contractions of finite groups of A,B,C,D Lie types

TL;DR

This paper develops supercharacter theories for finite groups derived from parabolic contractions of simple Lie groups of types A, B, C, D, classifying supercharacters and superclasses using rook placements in root systems.

Contribution

It introduces a new supercharacter theory framework for these groups based on combinatorial rook placements, extending previous theories to parabolic contractions.

Findings

Classified supercharacters and superclasses using rook placements

Constructed supercharacter theories for groups from Lie types A, B, C, D

Provided combinatorial tools for analyzing these finite groups

Abstract

We construct supercharacter theories for the finite groups constructed by parabolic constraction from simple groups of $A,B,C,D$ Lie types. In terms of rook placements in the root systems we classify supecharacters and superclasses.