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arXiv · 2105.04609

Combinatorial invariance conjecture for $\widetilde{A}_2$

Gaston Burrull·Nicolas Libedinsky·David Plaza
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Abstract

The combinatorial invariance conjecture (due independently to G. Lusztig and M. Dyer) predicts that if $[x,y]$ and $[x',y']$ are isomorphic Bruhat posets (of possibly different Coxeter systems), then the corresponding Kazhdan-Lusztig polynomials are equal, that is, $P_{x,y}(q)=P_{x',y'}(q)$. We prove this conjecture for the affine Weyl group of type $\widetilde{A}_2$. This is the first infinite group with non-trivial Kazhdan-Lusztig polynomials where the conjecture is proved.

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BibTeXRIS

Gaston Burrull, Nicolas Libedinsky, David Plaza. 2021-05-10. Combinatorial invariance conjecture for $\widetilde{A}_2$. https://doi.org/10.1093/imrn/rnac105

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