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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2111.12190 |
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| _version_ | 1866915110850658304 |
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| author | Elias, Ben Jensen, Lars Thorge Gibson, Joel |
| author_facet | Elias, Ben Jensen, Lars Thorge Gibson, Joel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_12190 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Categorical diagonalization and $p$-cells Elias, Ben Jensen, Lars Thorge Gibson, Joel Representation Theory 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. |
| title | Categorical diagonalization and $p$-cells |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2111.12190 |