%0 Generic %1 burrull2021combinatorial %A Burrull, Gaston %A Libedinsky, Nicolas %A Plaza, David %D 2021 %K KL invariance perverse %R 10.1093/imrn/rnac105 %T Combinatorial invariance conjecture for $A_2$ %U http://arxiv.org/abs/2105.04609 %X 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 $A_2$. This is the first infinite group with non-trivial Kazhdan-Lusztig polynomials where the conjecture is proved.

@misc{burrull2021combinatorial, 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.}, added-at = {2022-05-13T16:48:43.000+0200}, author = {Burrull, Gaston and Libedinsky, Nicolas and Plaza, David}, biburl = {https://www.bibsonomy.org/bibtex/27d8138ec44c905507cdd897c801f67d9/dragosf}, description = {Combinatorial invariance conjecture for $\widetilde{A}_2$}, doi = {10.1093/imrn/rnac105}, interhash = {de26bfa7e37e52ef42e1fa453a5ea306}, intrahash = {7d8138ec44c905507cdd897c801f67d9}, keywords = {KL invariance perverse}, note = {cite arxiv:2105.04609Comment: 21 pages, 9 colored figures. The new Preliminaries section includes the new Proposition 2.5 which simplifies the proof of the Main Theorem. New background material for the affine Weyl group was included. The old Appendix was replaced by the proofs of Propositions 3.1 and 3.3 in greater detail. The acknowledgments section was added. Final version}, timestamp = {2022-05-13T16:48:43.000+0200}, title = {Combinatorial invariance conjecture for $\widetilde{A}_2$}, url = {http://arxiv.org/abs/2105.04609}, year = 2021 }