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July 7, 2026Selecta Mathematica0 citationsOpen Access

Relative Serre duality for Hecke categories

QHQuoc P. HoPLPenghui Li

Key Points

  • The aim is to prove a conjecture regarding the relationship between adjoints of the parabolic induction functor in Hecke categories.
  • Proved conjecture of Gorsky et al. in the case of Weyl groups.
  • Showed the difference between left and right adjoints using relative full twist.
  • Established relative Serre duality pattern in Hecke categories.
  • Demonstrated the interrelation of functor adjoints in this mathematical structure.

Abstract

Abstract 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.

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Cite This Study

Ho et al. (2026) studied this question.

synapsesocial.com/papers/6a4c9687331bc25c9e5f3e02https://doi.org/10.1007/s00029-026-01175-5
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