We show that a symmetry property that we call the up-down symmetry implies that the Kazhdan–Lusztig Rx-polynomials of a pircon P are a P-kernel, and we show that this property holds in the classical cases. Then, we enhance and extend to this context a duality of Deodhar in parabolic Kazhdan–Lusztig theory.
Pircon kernels and up-down symmetry / Caselli, F.; Marietti, M.. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - STAMPA. - 565:(2021), pp. 324-352. [10.1016/j.jalgebra.2020.09.007]