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Are Kazhdan-Lusztig $R$-polynomials the Poincare polynomials of the corresponding affine varieties

Let $x$ and $y$ be two elements of $S_n$. Let $U(x,y)$ be the intersection $(BxB \cap B_{-} y B)/B$ inside the flag variety. Here $B$ and $B_{-}$ are the groups of upper and lower-triangular matrices ...