[Calcul localisé pour la catégorie de Hecke]
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.
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.
Keywords: Hecke category, localization, diagrammatic algebra
Mots-clés : catégorie de Hecke, localisation, algèbre diagrammatique
Elias, Ben 1 ; Williamson, Geordie 2
CC-BY 4.0
@article{AMBP_2023__30_1_1_0,
author = {Elias, Ben and Williamson, Geordie},
title = {Localized calculus for the {Hecke} category},
journal = {Annales math\'ematiques Blaise Pascal},
pages = {1--73},
year = {2023},
publisher = {Universit\'e Clermont Auvergne, Laboratoire de math\'ematiques Blaise Pascal},
volume = {30},
number = {1},
doi = {10.5802/ambp.415},
language = {en},
url = {https://www.numdam.org/articles/10.5802/ambp.415/}
}
TY - JOUR AU - Elias, Ben AU - Williamson, Geordie TI - Localized calculus for the Hecke category JO - Annales mathématiques Blaise Pascal PY - 2023 SP - 1 EP - 73 VL - 30 IS - 1 PB - Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal UR - https://www.numdam.org/articles/10.5802/ambp.415/ DO - 10.5802/ambp.415 LA - en ID - AMBP_2023__30_1_1_0 ER -
%0 Journal Article %A Elias, Ben %A Williamson, Geordie %T Localized calculus for the Hecke category %J Annales mathématiques Blaise Pascal %D 2023 %P 1-73 %V 30 %N 1 %I Université Clermont Auvergne, Laboratoire de mathématiques Blaise Pascal %U https://www.numdam.org/articles/10.5802/ambp.415/ %R 10.5802/ambp.415 %G en %F AMBP_2023__30_1_1_0
Elias, Ben; Williamson, Geordie. Localized calculus for the Hecke category. Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 1, pp. 1-73. doi: 10.5802/ambp.415
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