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Evaluation birepresentations of affine type a soergel bimodules

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dc.contributor.authorMackaay, Marco
dc.contributor.authorMiemietz, Vanessa
dc.contributor.authorVaz, Pedro
dc.date.accessioned2024-03-22T11:35:22Z
dc.date.available2024-03-22T11:35:22Z
dc.date.issued2024
dc.description.abstractIn this paper, we use Soergel calculus to define a monoidal functor, called the evaluation functor, from extended affine type A Soergel bimodules to the homotopy category of bounded complexes in finite type A Soergel bimodules. This functor categorifies the well-known evaluation homomorphism from the extended affine type A Hecke algebra to the finite type A Hecke algebra. Through it, one can pull back the triangulated birepresentation induced by any finitary birepresentation of finite type A Soergel bimodules to obtain a triangulated birepresentation of extended affine type A Soergel bimodules. We show that if the initial finitary birepresentation in finite type A is a cell birepresentation, the evaluation birepresentation in extended affine type A has a finitary cover, which we illustrate by working out the case of cell birepresentations with subregular apex in detail. (c) 2023 Elsevier Inc. All rights reserved.pt_PT
dc.description.sponsorshipEP/S017216/1; MIS-F.4536.19pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.doi10.1016/j.aim.2023.109401pt_PT
dc.identifier.issn0001-8708
dc.identifier.urihttp://hdl.handle.net/10400.1/20536
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherElsevierpt_PT
dc.relationCenter for Mathematical Analysis, Geometry and Dynamical Systems
dc.relationHigher Structures and Applications
dc.subjectEvaluation mappt_PT
dc.subjectEvaluation functorpt_PT
dc.subjectBirepresentationspt_PT
dc.subjectSoergel categorypt_PT
dc.titleEvaluation birepresentations of affine type a soergel bimodulespt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleCenter for Mathematical Analysis, Geometry and Dynamical Systems
oaire.awardTitleHigher Structures and Applications
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UID%2FMAT%2F04459%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-PUR%2F31089%2F2017/PT
oaire.citation.startPage109401pt_PT
oaire.citation.titleAdvances in Mathematicspt_PT
oaire.citation.volume436pt_PT
oaire.fundingStream6817 - DCRRNI ID
oaire.fundingStream3599-PPCDT
person.familyNameMACKAAIJ
person.givenNameMARCO
person.identifier.ciencia-idF810-F5CB-9F35
person.identifier.orcid0000-0001-9807-6991
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsrestrictedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication62310e63-1319-4bf3-87c8-1f6790d9f190
relation.isAuthorOfPublication.latestForDiscovery62310e63-1319-4bf3-87c8-1f6790d9f190
relation.isProjectOfPublicationab6441e5-1f82-452c-86ad-05969ba843b5
relation.isProjectOfPublication229dabb8-17af-4c32-a987-fae1a738940a
relation.isProjectOfPublication.latestForDiscovery229dabb8-17af-4c32-a987-fae1a738940a

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