On character degrees of cyclic and Klein four defect blocks

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Character degrees are confirmed for cyclic and Klein four defect blocks, enhancing understanding of modular representation.
Key evidence includes the affirmation of a conjecture by Giannelli regarding these specific characters.
Evaluation of character degrees associated with cyclic groups and Klein four groups demonstrates important relationships.
This finding supports the theory behind defect groups in modular representation, suggesting broader applications in algebra.

Implication

This report shows that a conjecture on character degrees holds for defect groups, indicating foundational implications for group theory.

We show that a conjecture of Giannelli on the degrees of height zero characters holds for blocks with a cyclic or Klein four defect group.

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Markus Linckelmann (2025) studied this question.

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This report shows that a conjecture on character degrees holds for defect groups, indicating foundational implications for group theory.

We show that a conjecture of Giannelli on the degrees of height zero characters holds for blocks with a cyclic or Klein four defect group.