Proposes conjectures using nonvanishing character sets Irr^x(G) and subnormalizers Sub_G(x) to address Alperin's Main Problem, recovering McKay's conjecture as a special case and verifying the main ones for simple groups with TI Sylow p-subgroups.
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math.RT 4years
2026 4verdicts
UNVERDICTED 4roles
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Derives generic character bijections for unipotent characters of nearly simple groups of Lie type that satisfy the subnormaliser conjecture when Sylow subgroups are abelian.
Establishes the strong subnormalizer conjecture for p-solvable groups with odd p under stated conditions and obtains new Glauberman correspondence results.
Conjectures propose that the sets Irr^x(G) and subgroups Sub_G(x) are the natural objects attached to p-elements x for studying local character values in block theory.
citing papers explorer
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Alperin's Main Problem of Block Theory
Proposes conjectures using nonvanishing character sets Irr^x(G) and subnormalizers Sub_G(x) to address Alperin's Main Problem, recovering McKay's conjecture as a special case and verifying the main ones for simple groups with TI Sylow p-subgroups.
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The subnormaliser conjecture and unipotent characters
Derives generic character bijections for unipotent characters of nearly simple groups of Lie type that satisfy the subnormaliser conjecture when Sylow subgroups are abelian.
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Subnormalizers and character correspondences in $p$-solvable groups
Establishes the strong subnormalizer conjecture for p-solvable groups with odd p under stated conditions and obtains new Glauberman correspondence results.
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The Main Problem of Block Theory: Picky Elements and Subnormalizers
Conjectures propose that the sets Irr^x(G) and subgroups Sub_G(x) are the natural objects attached to p-elements x for studying local character values in block theory.