Published January 1, 2025
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Weight conjectures for Parker-Semeraro fusion systems
- 1. Univ Manchester, Dept Math, Manchester M13 9PL, England
- 2. Loughborough Univ, Dept Math, Loughborough LE11 3TU, England
- 3. Tech Univ Dresden, Fac Math, D-01062 Dresden, Germany
- 4. Mimar Sinan Fine Arts Univ, Dept Math, TR-34380 Istanbul, Turkiye
Description
We prove that the Parker-Semeraro systems satisfy six of the nine Kessar-Linckelmann-Lynd-Semeraro weight conjectures for saturated fusion systems. As a by-product we obtain that Robinson's ordinary weight conjecture holds for the principal 3-block of Aut(G2(3)), the principal 5-blocks of HN, BM, Aut(HN), Ly, the principal 7-block of M, and the principal p-blocks of G2(p) for p >= 3. (c) 2025 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
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