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Session S10 - Categorification, Higher Representation Theory, and Homological Knot Invariants

Friday, July 16, 18:35 ~ 19:10 UTC-3

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

David Plaza

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, i.e., $P_{x,y}(q)=P_{x',y'}(q)$. In this talk we prove this conjecture for the affine Weyl group of type $\widetilde{A}_2$. This is the first non-trivial case where this conjecture is verified for an infinite group.