Strong Gelfand pairs of SL(2, pⁿ)

Abstract

A strong Gelfand pair (G, H) is a group G together with a subgroup H such that every irreducible character of H induces a multiplicity-free character of G. We classify the strong Gelfand pairs of the special linear groups $\text{SL}(2,p^n)$ where p is a prime.

Keywords:

• Characters
• finite groups
• special linear group
• strong Gelfand pair
• upper triangular group

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20G40
• Secondary: 20C15
• 20G05

Acknowledgments

All computations were made using Magma [14]. The authors also thank the referee for useful comments.