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arXiv · 2111.12190

Categorical diagonalization and $p$-cells

Ben Elias·Lars Thorge Jensen·Joel Gibson
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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 $A$. In this paper we make analogous conjectures for the $p$-canonical basis, and the Hecke category in characteristic $p$. We prove the categorified conjecture in type $C_2$, 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.

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BibTeXRIS

Ben Elias, Lars Thorge Jensen, Joel Gibson. 2021-11-23. Categorical diagonalization and $p$-cells. https://doi.org/10.4310/pamq.241203033151

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