Abstract
We prove a duality result for the parabolic Kazhdan–Lusztig R-polynomials of a finite Coxeter system. This duality is similar to, but different from, the one obtained in [9]. As a consequence of our duality we obtain an identity between the parabolic Kazhdan–Lusztig and inverse Kazhdan–Lusztig polynomials of a finite Coxeter system. We also obtain applications to certain modules defined by Deodhar and derive a result that gives evidence in favor of Marietti's combinatorial invariance conjecture for parabolic Kazhdan–Lusztig polynomials.
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