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### Degeneration of modules over the affine symmetric group and jeu de taquin

Let $H_n$ be the group algebra of the affine Coxeter group of type A (feel free to replace it by the affine Hecke algebra). This is generated by elements $y_i$'s, $i=1,\dots,n$ and transpositions ...

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### When are parabolic Kazhdan-Lusztig polynomials nonzero?

Let $W$ be a Coxeter group with simple reflections $S$ and let $J \subseteq S$. Let $P^J_{\tau, \sigma}$ be the parabolic Kazhdan-Lusztig polynomials in the case $u = q$ in the sense of On Some ...