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

Abstract

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 $S_n$. This significantly generalizes the main previously-known case of the conjecture, that of lower intervals.

arXiv commentv4: updated title; v5: final version, to appear in Mathematische Annalen

References in corpus (3)

• The full Kostant-Toda hierarchy on the positive flag variety
• Towards combinatorial invariance for Kazhdan-Lusztig polynomials
• A combinatorial formula for the coefficient of $q$ in Kazhdan-Lusztig polynomials

Cited by in corpus (2)

• On combinatorial invariance of parabolic Kazhdan-Lusztig polynomials
• The BBDVW Conjecture for Kazhdan-Lusztig polynomials of lower intervals