Pircon kernels and up-down symmetry

Abstract

We show that a symmetry property that we call the up-down symmetry implies that the Kazhdan--Lusztig $R^x$-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.

to appear in Journal of Algebra. arXiv admin note: substantial text overlap with arXiv:1907.00858

References in corpus (2)

• Special matchings in Coxeter groups
• Kazhdan-Lusztig R-polynomials for pircons