Affinizations, R-matrices and reflection functors

Masaki Kashiwara; Myungho Kim; Se jin Oh; Euiyong Park

doi:10.1016/j.aim.2024.109598

Affinizations, R-matrices and reflection functors

Masaki Kashiwara
, Myungho Kim
, Se jin Oh
, Euiyong Park

Department of Mathematics

Kyoto University
Korea Institute for Advanced Study
Kyung Hee University
Sungkyunkwan University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

In this paper we establish affinizations and R-matrices in the language of pro-objects, and as an application, we construct reflection functors over the localizations of quiver Hecke algebras of arbitrary finite types. This reflection functor categorifies the braid group action on the half of a quantum group and the Saito reflection.

Original language	English
Article number	109598
Journal	Advances in Mathematics
Volume	443
DOIs	https://doi.org/10.1016/j.aim.2024.109598
State	Published - May 2024

Keywords

Affinization
Localization
Quiver Hecke algebra
R-matrices
Reflection

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10.1016/j.aim.2024.109598

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title = "Affinizations, R-matrices and reflection functors",

abstract = "In this paper we establish affinizations and R-matrices in the language of pro-objects, and as an application, we construct reflection functors over the localizations of quiver Hecke algebras of arbitrary finite types. This reflection functor categorifies the braid group action on the half of a quantum group and the Saito reflection.",

keywords = "Affinization, Localization, Quiver Hecke algebra, R-matrices, Reflection",

author = "Masaki Kashiwara and Myungho Kim and Oh, \{Se jin\} and Euiyong Park",

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AU - Kashiwara, Masaki

AU - Kim, Myungho

AU - Oh, Se jin

AU - Park, Euiyong

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N2 - In this paper we establish affinizations and R-matrices in the language of pro-objects, and as an application, we construct reflection functors over the localizations of quiver Hecke algebras of arbitrary finite types. This reflection functor categorifies the braid group action on the half of a quantum group and the Saito reflection.

AB - In this paper we establish affinizations and R-matrices in the language of pro-objects, and as an application, we construct reflection functors over the localizations of quiver Hecke algebras of arbitrary finite types. This reflection functor categorifies the braid group action on the half of a quantum group and the Saito reflection.

KW - Affinization

KW - Localization

KW - Quiver Hecke algebra

KW - R-matrices

KW - Reflection

UR - https://www.scopus.com/pages/publications/85187706209

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DO - 10.1016/j.aim.2024.109598

M3 - Article

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VL - 443

JO - Advances in Mathematics

JF - Advances in Mathematics

M1 - 109598

ER -

Affinizations, R-matrices and reflection functors

Abstract

Keywords

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