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<p>Trinh and Xue have proposed a startling conjecture on intersections of blocks of cyclotomic Hecke algebras occurring in modular representation theory of finite reductive groups. We prove this conjecture for all exceptional type groups apart from a few situations in type <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(E_8\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>E</mi> <mn>8</mn> </msub> </math></EquationSource> </InlineEquation>. We also give a conceptual proof in all cases where relative Weyl groups are cyclic. Furthermore, we propose several generalisations, to Suzuki and Ree groups, to non-rational Coxeter groups and even more generally to spetsial complex reflection groups, and confirm these in various cases.</p>

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Intersections of blocks of cyclotomic Hecke algebras

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月7日

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  • Maria Chlouveraki,
  • Gunter Malle

摘要

Trinh and Xue have proposed a startling conjecture on intersections of blocks of cyclotomic Hecke algebras occurring in modular representation theory of finite reductive groups. We prove this conjecture for all exceptional type groups apart from a few situations in type \(E_8\) E 8 . We also give a conceptual proof in all cases where relative Weyl groups are cyclic. Furthermore, we propose several generalisations, to Suzuki and Ree groups, to non-rational Coxeter groups and even more generally to spetsial complex reflection groups, and confirm these in various cases.