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<p>We show that the <i>Combinatorial Invariance Conjecture</i> for Kazhdan–Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic version that we introduce, are equivalent. We use this to give a new proof of Marietti’s conjecture in the case of lower Bruhat intervals and to prove several new cases of the parabolic conjectures.</p>

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On combinatorial invariance of parabolic Kazhdan–Lusztig polynomials

  • 期刊论文

  • 发表日期：

    2025年5月28日

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  • Grant T. Barkley,
  • Christian Gaetz

摘要

We show that the Combinatorial Invariance Conjecture for Kazhdan–Lusztig polynomials due to Lusztig and to Dyer, its parabolic analog due to Marietti, and a refined parabolic version that we introduce, are equivalent. We use this to give a new proof of Marietti’s conjecture in the case of lower Bruhat intervals and to prove several new cases of the parabolic conjectures.