Skew characters which contain only few components

TL;DR

This paper addresses errors in previous proofs related to skew characters with few components, clarifying the correct results and indicating ongoing work to rectify the theoretical proofs.

Contribution

It corrects earlier mistakes in the proofs of key theorems about skew characters, providing accurate results and outlining future work for complete validation.

Findings

Corrected proof of Lemma 3.6 is in preparation

Section 3 results are valid except Theorem 3.12

Ongoing work to finalize the proof corrections

Abstract

Wrong assumptions were made in the proof of Theorem 3.12 and Lemma 3.6. A preprint containing a correct proof for Lemma 3.6 is in preparation and will be uploaded later this month. So the results of section 3 are correct, apart from Theorem 3.12 and the remarks following Theorem 3.12.