Decomposition numbers of SO_7(q) and Sp_6(q)

TL;DR

This paper determines the modular decomposition numbers for unipotent characters in the principal blocks of SO_7(q) and Sp_6(q) across all prime powers q and odd primes l, advancing understanding in modular representation theory.

Contribution

It completes the calculation of l-modular decomposition numbers for specific classical groups, filling a gap in the existing literature.

Findings

Decomposition numbers for SO_7(q) and Sp_6(q) are fully determined.

Results hold for all prime powers q and odd primes l.

Enhances the understanding of modular representations of classical groups.

Abstract

We complete the l-modular decomposition numbers of the unipotent characters in the principal block of the special orthogonal groups SO_7(q) and the symplectic groups Sp_6(q) for all prime powers q and all odd primes l different from the defining characteristic.