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Length of the product of two elements of the subregular two-sided cell in the affine Weyl group of type A
The affine Weyl group of type $A_n$ can be described as follows. It is the group of all permutations $\sigma: \mathbb Z \to \mathbb Z$ such that $\sigma(i+n)=\sigma(i)+n$ and $\sum_{i=1}^n (\sigma(i)-...