Categorical diagonalization and $p$-cells
Abstract
In the Iwahori-Hecke algebra, the full twist acts on cell modules by a scalar, and the half twist acts by a scalar and an involution. A categorification of this statement, describing the action of the half and full twist Rouquier complexes on the Hecke category, was conjectured by Elias-Hogancamp, and proven in type . In this paper we make analogous conjectures for the -canonical basis, and the Hecke category in characteristic . We prove the categorified conjecture in type , where the situation is already interesting. The decategorified conjecture is confirmed by computer in rank at most 6; information is found in the appendix, written by Joel Gibson.
Cite
@article{arxiv.2111.12190,
title = {Categorical diagonalization and $p$-cells},
author = {Ben Elias and Lars Thorge Jensen and Joel Gibson},
journal= {arXiv preprint arXiv:2111.12190},
year = {2025}
}
Comments
Paper by Elias and Jensen, with appendix by Gibson. 45 pages plus 8 page appendix. Many figures, color viewing important for the computational chapters. Supplemental computations currently found at https://pages.uoregon.edu/belias/TypeC2OverZ.pdf