Papers › Categorical diagonalization and p-cells
Categorical diagonalization and p-cells
Ben Elias, Lars Thorge Jensen, Joel Gibson
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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 C₂, 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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