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<p>We prove a conjecture of Gorsky, Hogancamp, Mellit, and Nakagane in the Weyl group case. Namely, we show that the left and right adjoints of the parabolic induction functor between the associated Hecke categories of Soergel bimodules differ by the relative full twist. This exhibits a relative Serre duality pattern for the Hecke categories.</p>

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Relative Serre duality for Hecke categories

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月5日

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  • Quoc P. Ho,
  • Penghui Li

摘要

We prove a conjecture of Gorsky, Hogancamp, Mellit, and Nakagane in the Weyl group case. Namely, we show that the left and right adjoints of the parabolic induction functor between the associated Hecke categories of Soergel bimodules differ by the relative full twist. This exhibits a relative Serre duality pattern for the Hecke categories.