The Steinberg character in the principal block of a finite reductive group

Abstract

We give a generic description of the non-defining primes $\mathcal{l}$, for which the Steinberg character lies in the principal $\mathcal{l}$-block of a finite reductive group.

Keywords:

• Finite reductive group
• non-defining prime
• principal block
• Steinberg character

2020 Mathematics subject classification:

• 20C15
• 20C33

Acknowledgments

We are deeply grateful to the referees for their invaluable comments.

Additional information

Funding

The first author was supported by the National Key R&D Program of China (Grant No. 2020YFE0204200), and the second by NSFC (12171211).