English

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

Combinatorics 2025-11-04 v5 Representation Theory

Abstract

We adapt the hypercube decompositions introduced by Blundell-Buesing-Davies-Veli\v{c}kovi\'{c}-Williamson to prove the Combinatorial Invariance Conjecture for Kazhdan-Lusztig RR-polynomials in the case of elementary intervals in SnS_n. This significantly generalizes the main previously-known case of the conjecture, that of lower intervals.

Keywords

Cite

@article{arxiv.2303.15577,
  title  = {Combinatorial invariance for Kazhdan-Lusztig $R$-polynomials of elementary intervals},
  author = {Grant T. Barkley and Christian Gaetz},
  journal= {arXiv preprint arXiv:2303.15577},
  year   = {2025}
}

Comments

v4: updated title; v5: final version, to appear in Mathematische Annalen