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Kazhdan-Lusztig polynomials and drift configurations
The coefficients of the Kazhdan-Lusztig polynomials are
nonnegative integers that are upper semicontinuous on Bruhat order.
Conjecturally, the same properties hold for -polynomials of
local rings of Schubert varieties. This suggests a parallel between the two
families of polynomials. We prove our conjectures for Grassmannians, and more
generally, covexillary Schubert varieties in complete flag varieties, by
deriving a combinatorial formula for . We introduce \emph{drift
configurations} to formulate a new and compatible combinatorial rule for
. From our rules we deduce, for these cases, the coefficient-wise
inequality .Comment: 26 pages. To appear in Algebra & Number Theor
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