Modular representations of the ortho-symplectic supergroups

TL;DR

This paper constructs a Chevalley basis for ortho-symplectic Lie superalgebras, classifies simple modules over fields of prime characteristic, and establishes a Steinberg tensor product theorem for these supergroups.

Contribution

It introduces a Chevalley basis, classifies simple modules, and proves a Steinberg tensor product theorem for ortho-symplectic supergroups, advancing modular representation theory.

Findings

Constructed a Chevalley type integral basis.

Classified simple modules over algebraically closed fields of prime characteristic.

Proved a Steinberg tensor product theorem for the supergroup.

Abstract

A Chevalley type integral basis for the ortho-symplectic Lie superalgebra is constructed. The simple modules of the ortho-symplectic supergroup over an algebraically closed field of prime characteristic not equal to 2 are classified, where a key combinatorial ingredient comes from the Mullineux conjecture on modular representations of the symmetric group. A Steinberg tensor product theorem for the ortho-symplectic supergroup is also obtained.