Strong Gelfand Pairs of SL(2,p)

TL;DR

This paper classifies strong Gelfand pairs within SL(2,p), identifying subgroup structures that produce multiplicity-free induced characters, advancing understanding of representation theory in finite groups.

Contribution

It provides a complete classification of strong Gelfand pairs for SL(2,p), a previously unresolved problem in the representation theory of finite groups.

Findings

Identified all subgroups H of SL(2,p) forming strong Gelfand pairs.

Established criteria for multiplicity-free induction of characters from H to G.

Enhanced understanding of the structure of irreducible representations in SL(2,p).

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 SL(2, p) where p is a prime.