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.
Caselli F., Marietti M. (2021). Pircon kernels and up-down symmetry. JOURNAL OF ALGEBRA, 565, 324-352 [10.1016/j.jalgebra.2020.09.007].
Pircon kernels and up-down symmetry
Caselli F.
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2021
Abstract
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.File in questo prodotto:
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KL P polynomials for pirconsRevised.pdf
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