Parabolic Kazhdan-Lusztig R-polynomials for Hermitian symmetric pairs

We give explicit combinatorial product formulas for the parabolic Kazhdan-Lusztig R-polynomials of Hermitian symmetric pairs. Our results imply that all the roots of these polynomials are (either zero or) roots of unity, and complete those in [F. Brenti, Kazhdan-Lusztig and R-polynomials, Young's lattice, and Dyck partitions, Pacific J. Math. 207 (2002) 257-286] on Hermitian symmetric pairs of type A. As an application of our results, we derive explicit combinatorial product formulas for certain sums and alternating sums of ordinary Kazhdan-Lusztig R-polynomials. (c) 2007 Elsevier Inc. All rights reserved