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arXiv · 1410.2136

Graded cellularity and the Monotonicity Conjecture

David Plaza
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Abstract

The graded cellularity of Libedinsky Double Leaves, which form a basis for the endomorphism ring of the Bott_Samelson_Soergel bimodules, allows us to view the Kazhdan_Lusztig polynomials as graded decomposition numbers. Using this point of view, I provide in this paper a new proof of the monotonicity conjecture for the Kazhdan_Lusztig polynomials of any Coxeter system.

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David Plaza. 2014-10-08. Graded cellularity and the Monotonicity Conjecture. https://arxiv.org/abs/1410.2136

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