Publication
Trihedral Soergel bimodules
| dc.contributor.author | Mackaay, Marco | |
| dc.contributor.author | Mazorchuk, Volodymyr | |
| dc.contributor.author | Miemietz, Vanessa | |
| dc.contributor.author | Tubbenhauer, Daniel | |
| dc.date.accessioned | 2020-09-23T08:25:15Z | |
| dc.date.available | 2020-09-23T08:25:15Z | |
| dc.date.issued | 2018-04-24 | |
| dc.description.abstract | The quantum Satake correspondence relates dihedral Soergel bimodules to the semisimple quotient of the quantum $\mathfrak{sl}_2$ representation category. It also establishes a precise relation between the simple transitive $2$-representations of both monoidal categories, which are indexed by bicolored $\mathsf{ADE}$ Dynkin diagrams. Using the quantum Satake correspondence between affine $\mathsf{A}_{2}$ Soergel bimodules and the semisimple quotient of the quantum $\mathfrak{sl}_3$ representation category, we introduce trihedral Hecke algebras and Soergel bimodules, generalizing dihedral Hecke algebras and Soergel bimodules. These have their own Kazhdan-Lusztig combinatorics, simple transitive $2$-representations corresponding to tricolored generalized $\mathsf{ADE}$ Dynkin diagrams. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.doi | 10.4064/fm566-3-2019 | pt_PT |
| dc.identifier.issn | 0016-2736 | |
| dc.identifier.uri | http://hdl.handle.net/10400.1/14737 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
| dc.subject | 2-representation theory | pt_PT |
| dc.subject | Quantum groups and their fusion categories | pt_PT |
| dc.subject | Hecke algebras | pt_PT |
| dc.subject | Soergel bimodules | pt_PT |
| dc.subject | Zigzag algebras | pt_PT |
| dc.title | Trihedral Soergel bimodules | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F04459%2F2013/PT | |
| oaire.citation.endPage | 300 | pt_PT |
| oaire.citation.issue | 3 | pt_PT |
| oaire.citation.startPage | 219 | pt_PT |
| oaire.citation.title | Fundamenta Mathematicae | pt_PT |
| oaire.citation.volume | 248 | pt_PT |
| oaire.fundingStream | 5876 | |
| person.familyName | MACKAAIJ | |
| person.givenName | MARCO | |
| person.identifier.ciencia-id | F810-F5CB-9F35 | |
| person.identifier.orcid | 0000-0001-9807-6991 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
| relation.isAuthorOfPublication | 62310e63-1319-4bf3-87c8-1f6790d9f190 | |
| relation.isAuthorOfPublication.latestForDiscovery | 62310e63-1319-4bf3-87c8-1f6790d9f190 | |
| relation.isProjectOfPublication | 6760ef13-9949-4bc7-9636-5e2aec9cb619 | |
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