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<p>We adapt the <i>hypercube decompositions</i> introduced by Blundell–Buesing–Davies–Veličković–Williamson to prove the Combinatorial Invariance Conjecture for Kazhdan–Lusztig <i>R</i>-polynomials in the case of <i>elementary intervals</i> in <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3175_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(S_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>. This significantly generalizes the main previously-known case of the conjecture for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3175_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(S_n\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>S</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation>, that of lower intervals.</p>

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Combinatorial invariance for Kazhdan–Lusztig R-polynomials of elementary intervals

  • 期刊论文

  • 发表日期：

    2025年5月3日

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  • Grant T. Barkley,
  • Christian Gaetz

摘要

We adapt the hypercube decompositions introduced by Blundell–Buesing–Davies–Veličković–Williamson to prove the Combinatorial Invariance Conjecture for Kazhdan–Lusztig R-polynomials in the case of elementary intervals in \(S_n\) S n . This significantly generalizes the main previously-known case of the conjecture for \(S_n\) S n , that of lower intervals.