Koszul duality for Coxeter groups

Autores
Riche, Simon; Vay, Cristian Damian
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We construct a “Koszul duality” equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a construction of Beĭlinson–Ginzburg–Soergel [8] and Bezrukavnikov–Yun [9] in a geometric context, and of the first author with Achar, Makisumi and Williamson [4]. As an application, we show that the combinatorics of the “tilting perverse sheaves” considered in [6] is encoded in the combinatorics of the canonical basis of the Hecke algebra of (W,S) attached to the dual realization.
Fil: Riche, Simon. Centre National de la Recherche Scientifique; Francia
Fil: Vay, Cristian Damian. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
Materia
KOSZUL DUALITY
COXETER GROUPS
ELIAS-WILLIAMSON DIAGRAMATIC CATEGORIES
PERVERSE SHEAVES
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/257068
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/257068
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Koszul duality for Coxeter groupsRiche, SimonVay, Cristian DamianKOSZUL DUALITYCOXETER GROUPSELIAS-WILLIAMSON DIAGRAMATIC CATEGORIESPERVERSE SHEAVEShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We construct a “Koszul duality” equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a construction of Beĭlinson–Ginzburg–Soergel [8] and Bezrukavnikov–Yun [9] in a geometric context, and of the first author with Achar, Makisumi and Williamson [4]. As an application, we show that the combinatorics of the “tilting perverse sheaves” considered in [6] is encoded in the combinatorics of the canonical basis of the Hecke algebra of (W,S) attached to the dual realization.Fil: Riche, Simon. Centre National de la Recherche Scientifique; FranciaFil: Vay, Cristian Damian. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; ArgentinaNorwegian University of Science and Technology2024-05info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/257068Riche, Simon; Vay, Cristian Damian; Koszul duality for Coxeter groups; Norwegian University of Science and Technology; Annals of Representation Theory; 1; 3; 5-2024; 335-3742704-2081CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://art.centre-mersenne.org/articles/10.5802/art.10/info:eu-repo/semantics/altIdentifier/doi/10.5802/art.10info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T09:55:47Zoai:ri.conicet.gov.ar:11336/257068instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 09:55:47.328CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Koszul duality for Coxeter groups
title Koszul duality for Coxeter groups
spellingShingle Koszul duality for Coxeter groups
Riche, Simon
KOSZUL DUALITY
COXETER GROUPS
ELIAS-WILLIAMSON DIAGRAMATIC CATEGORIES
PERVERSE SHEAVES
title_short Koszul duality for Coxeter groups
title_full Koszul duality for Coxeter groups
title_fullStr Koszul duality for Coxeter groups
title_full_unstemmed Koszul duality for Coxeter groups
title_sort Koszul duality for Coxeter groups
dc.creator.none.fl_str_mv Riche, Simon
Vay, Cristian Damian
author Riche, Simon
author_facet Riche, Simon
Vay, Cristian Damian
author_role author
author2 Vay, Cristian Damian
author2_role author
dc.subject.none.fl_str_mv KOSZUL DUALITY
COXETER GROUPS
ELIAS-WILLIAMSON DIAGRAMATIC CATEGORIES
PERVERSE SHEAVES
topic KOSZUL DUALITY
COXETER GROUPS
ELIAS-WILLIAMSON DIAGRAMATIC CATEGORIES
PERVERSE SHEAVES
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We construct a “Koszul duality” equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a construction of Beĭlinson–Ginzburg–Soergel [8] and Bezrukavnikov–Yun [9] in a geometric context, and of the first author with Achar, Makisumi and Williamson [4]. As an application, we show that the combinatorics of the “tilting perverse sheaves” considered in [6] is encoded in the combinatorics of the canonical basis of the Hecke algebra of (W,S) attached to the dual realization.
Fil: Riche, Simon. Centre National de la Recherche Scientifique; Francia
Fil: Vay, Cristian Damian. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
description We construct a “Koszul duality” equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a construction of Beĭlinson–Ginzburg–Soergel [8] and Bezrukavnikov–Yun [9] in a geometric context, and of the first author with Achar, Makisumi and Williamson [4]. As an application, we show that the combinatorics of the “tilting perverse sheaves” considered in [6] is encoded in the combinatorics of the canonical basis of the Hecke algebra of (W,S) attached to the dual realization.
publishDate 2024
dc.date.none.fl_str_mv 2024-05
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/257068
Riche, Simon; Vay, Cristian Damian; Koszul duality for Coxeter groups; Norwegian University of Science and Technology; Annals of Representation Theory; 1; 3; 5-2024; 335-374
2704-2081
CONICET Digital
CONICET
url http://hdl.handle.net/11336/257068
identifier_str_mv Riche, Simon; Vay, Cristian Damian; Koszul duality for Coxeter groups; Norwegian University of Science and Technology; Annals of Representation Theory; 1; 3; 5-2024; 335-374
2704-2081
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://art.centre-mersenne.org/articles/10.5802/art.10/
info:eu-repo/semantics/altIdentifier/doi/10.5802/art.10
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Norwegian University of Science and Technology
publisher.none.fl_str_mv Norwegian University of Science and Technology
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1844613679405858816
score 13.070432

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