Zusammenfassung
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.
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