Annales Mathématiques
Blaise Pascal
no. 1
Localized calculus for the Hecke category
[Calcul localisé pour la catégorie de Hecke]
Ben Elias1 ; Geordie Williamson2
1 Department of Mathematics University of Oregon 1585 E 13th Ave, Eugene, OR 97403 USA
2 Sydney Mathematical Research Institute School of Mathematics and Statistics Faculty of Science Room L4.44, Quadrangle A14 The University of Sydney, NSW, 2006 AUSTRALIA
Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 1, pp. 1-73.

Nous construisons un foncteur de la catégorie de Hecke vers un groupoïde construit à partir du groupe de Coxeter sous-jacent. Cette construction corrige une lacune dans un travail antérieur des auteurs. Ce foncteur fournit une réalisation abstraite de la localisation de la catégorie de Hecke en le corps des fractions. Connaître des formules explicites pour la localisation est un outil technique clé pour le calcul algorithmique avec les bimodules de Soergel.

We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke category at the field of fractions. Knowing explicit formulas for the localization is a key technical tool in software for computations with Soergel bimodules.

Publié le :
DOI : 10.5802/ambp.415
Classification : 00X99
Keywords: Hecke category, localization, diagrammatic algebra
Mot clés : catégorie de Hecke, localisation, algèbre diagrammatique
Ben Elias 1 ; Geordie Williamson 2

1 Department of Mathematics University of Oregon 1585 E 13th Ave, Eugene, OR 97403 USA
2 Sydney Mathematical Research Institute School of Mathematics and Statistics Faculty of Science Room L4.44, Quadrangle A14 The University of Sydney, NSW, 2006 AUSTRALIA
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Ben Elias; Geordie Williamson. Localized calculus for the Hecke category. Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 1, pp. 1-73. doi : 10.5802/ambp.415. https://ambp.centre-mersenne.org/articles/10.5802/ambp.415/

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