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Revista Colombiana de Matemáticas

Print version ISSN 0034-7426

Rev.colomb.mat. vol.53  supl.1 Bogotá Dec. 2019  Epub Mar 24, 2020

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

Artículos originales

On monoidal Koszul duality for the Hecke category

Shotaro Makisumi1  * 

1 Columbia University, New York


Abstract:

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.

Keywords: Hecke algebra; Hecke category; Soergel bimodules; Koszul duality

Resumen:

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.

Palabras clave: Álgebra de Hecke; categoría de Hecke; bimódulos de Soergel; dualidad de Koszul

Text complete and PDF

References

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Received: June 30, 2018; Accepted: February 16, 2019

*Correspondencia: Shotaro Makisumi, Department of Mathematics, Columbia University, 2990 Broadway, New York, NY 10027, United States. Correo electrónico: makisumi@math.columbia.edu. DOI: https://doi.org/10.15446/recolma.v53nsupl.84084

2010 Mathematics Subject Classification. 20F55, 20C08, 20G05

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