Cristian Lenart, Kirill Zainoulline
We study the equivariant oriented cohomology ring hT (G/P ) of partial flag varieties using the moment map approach. Our objective is to define the right Hecke action on this cohomology ring and prove that the respective Bott-Samelson classes in hT (G/P ) can be obtained by applying this action to the fundamental class of the identity point, thus generalizing previous results by Brion, Knutson, Peterson, Tymoczko, and others. The methodology involves focusing on the equivariant oriented cohomology theory corresponding to the 2-parameter Todd genus, providing a new interpretation of Deodhar’s construction of the parabolic Kazhdan-Lusztig basis. Based on this interpretation, we define the parabolic Kazhdan-Lusztig (KL) Schubert classes independently of a reduced word and make a positivity conjecture, along with a conjecture regarding the relationship of these classes to the smoothness of Schubert varieties. We conclude by proving several special cases of our conjectures.
@article{c664b5de-39cf-4d9e-8a3b-97fb497179dc,
title={Parabolic Kazhdan Lusztig Basis Schubert},
author={Cristian Lenart and Kirill Zainoulline},
year={2026},
language={en}
}TY - JOUR TI - Parabolic Kazhdan Lusztig Basis Schubert AU - Cristian Lenart AU - Kirill Zainoulline PY - 2026 LA - en ER -
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