On monoidal Koszul duality for the Hecke category

Shotaro Makisumi

doi:10.15446/recolma.v53nsupl.84084

Publicado

2019-12-11

On monoidal Koszul duality for the Hecke category

DOI:

https://doi.org/10.15446/recolma.v53nsupl.84084

Palabras clave:

Hecke algebra, Hecke category, Soergel bimodules, Koszul duality (en)
Álgebra de Hecke, categoría de Hecke, bimódulos de Soergel, dualidad de Koszul (es)

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Autores/as

Shotaro Makisumi Columbia University

Resumen (en)
Resumen (es)

We attempt to give a gentle (though ahistorical) introduction to Koszul duality phenomena for the Hecke category, focusing on the form of this duality studied in joint work [1, 2] of Achar, Riche, Williamson, and the author. We illustrate some key phenomena and constructions for the simplest nontrivial case of (finite) SL₂ using Soergel bimodules, a concrete algebraic model of the Hecke category.

Procuramos dar una amable, si bien ahistórica, introducción a los fenómenos de dualidad de Koszul en la categoría de Hecke, con foco en la forma de esta dualidad estudiada en los trabajos [1, 2] en colaboración con Achar, Riche y Williamson. Ilustramos algunos fenómenos y construcciones claves en el ejemplo no trivial más simple, SL₂ finito, usando bimódulos de Soergel, un modelo algebraico concreto de la categoría de Hecke.

Referencias

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Cómo citar

APA

Makisumi, S. (2019). On monoidal Koszul duality for the Hecke category. Revista Colombiana de Matemáticas, 53(supl), 195–222. https://doi.org/10.15446/recolma.v53nsupl.84084

ACM

[1]

Makisumi, S. 2019. On monoidal Koszul duality for the Hecke category. Revista Colombiana de Matemáticas. 53, supl (dic. 2019), 195–222. DOI:https://doi.org/10.15446/recolma.v53nsupl.84084.

ACS

(1)

Makisumi, S. On monoidal Koszul duality for the Hecke category. rev.colomb.mat 2019, 53, 195-222.

ABNT

MAKISUMI, S. On monoidal Koszul duality for the Hecke category. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. supl, p. 195–222, 2019. DOI: 10.15446/recolma.v53nsupl.84084. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/84084. Acesso em: 22 ene. 2025.

Chicago

Makisumi, Shotaro. 2019. «On monoidal Koszul duality for the Hecke category». Revista Colombiana De Matemáticas 53 (supl):195-222. https://doi.org/10.15446/recolma.v53nsupl.84084.

Harvard

Makisumi, S. (2019) «On monoidal Koszul duality for the Hecke category», Revista Colombiana de Matemáticas, 53(supl), pp. 195–222. doi: 10.15446/recolma.v53nsupl.84084.

IEEE

[1]

S. Makisumi, «On monoidal Koszul duality for the Hecke category», rev.colomb.mat, vol. 53, n.º supl, pp. 195–222, dic. 2019.

MLA

Makisumi, S. «On monoidal Koszul duality for the Hecke category». Revista Colombiana de Matemáticas, vol. 53, n.º supl, diciembre de 2019, pp. 195-22, doi:10.15446/recolma.v53nsupl.84084.

Turabian

Makisumi, Shotaro. «On monoidal Koszul duality for the Hecke category». Revista Colombiana de Matemáticas 53, no. supl (diciembre 11, 2019): 195–222. Accedido enero 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/84084.

Vancouver

1.

Makisumi S. On monoidal Koszul duality for the Hecke category. rev.colomb.mat [Internet]. 11 de diciembre de 2019 [citado 22 de enero de 2025];53(supl):195-222. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/84084

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CrossRef Cited-by

2

1. Nicolas Libedinsky. (2022). IntroSurvey of Representation Theory. Journal of the Indian Institute of Science, 102(3), p.907. https://doi.org/10.1007/s41745-022-00301-4.

2. Ben Elias, Shotaro Makisumi, Ulrich Thiel, Geordie Williamson. (2020). Introduction to Soergel Bimodules. RSME Springer Series. 5, p.529. https://doi.org/10.1007/978-3-030-48826-0_26.