Odd Character Degrees for Sp(2n,2)

TL;DR

This paper investigates the McKay conjecture and the inductive McKay condition for symplectic groups over the field with two elements, providing verification for specific cases involving Sp(2n,2).

Contribution

It verifies the McKay conjecture for Sp(2n,2) and confirms the inductive McKay condition for Sp(4,2^m) across all primes, advancing understanding of these conjectures in finite groups.

Findings

McKay conjecture holds for Sp(2n,2).

Inductive McKay condition verified for Sp(4,2^m).

Results support the conjecture's validity in these cases.

Abstract

We check McKay conjecture on character degrees for the case of symplectic groups over the field with two elements Sp(2n,2) and the prime 2. Then we check the inductive McKay condition (Isaacs-Malle-Navarro 2007) for Sp(4,2^m) and all primes.