TL;DR
This paper computes p-Kazhdan-Lusztig bases for certain Hecke categories across all characteristics, revealing complex behaviors and introducing new concepts to explain them.
Contribution
It provides explicit p-Kazhdan-Lusztig bases for antispherical and spherical (co)minuscule Hecke categories, using geometric and diagrammatic techniques, and introduces notions of p-small resolutions and p-tight elements.
Findings
p-Kazhdan-Lusztig bases determined in all characteristics.
2-Kazhdan-Lusztig bases show pathological behavior.
Introduction of p-small resolutions and p-tight elements to explain phenomena.
Abstract
We determine the p-Kazhdan-Lusztig bases for antispherical (co)minuscule Hecke categories in all characteristics, and for spherical (co)minuscule Hecke categories in good characteristic. This is achieved using geometric and diagrammatic methods. The 2-Kazhdan-Lusztig bases of antispherical cominuscule Hecke categories exhibit extremely pathological behaviour. The notions of p-small resolutions and p-tight elements are introduced and conjecturally explain this behaviour.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models