Parabolic recursions for Kazhdan–Lusztig polynomials and the hypercube decomposition

• Maxim Gurevich ^[2] ; Chuijia Wang ^[1]
  1. [1] Chinese University of Hong Kong

     Chinese University of Hong Kong

     RAE de Hong Kong (China)

     
  2. [2] Department of Mathematics, Technion – Israel Institute of Technology, Haifa, Israel
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024, págs. 1-27
• Idioma: inglés
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• Resumen

  • We employ general parabolic recursion methods to demonstrate the recently devised hypercube formula for Kazhdan-Lusztig polynomials of Sn, and establish its generalization to the full setting of a finite Coxeter system through algebraic proof. We introduce procedures for positive decompositions of q-derived Kazhdan–Lusztig polynomials within this setting, that utilize classical Hecke algebra positivity phenomena of Dyer-Lehrer and Grojnowski–Haiman. This leads to a distinct algorithmic approach to the subject, based on induction from a parabolic subgroup. We propose suitable weak variants of the combinatorial invariance conjecture and verify their validity for permutation groups.