Localizations for quiver Hecke algebras III

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

doi:10.1007/s00208-024-02875-z

Localizations for quiver Hecke algebras III

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

Department of Mathematics

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

Abstract

Let R be a quiver Hecke algebra, and let C_w,v be the category of finite-dimensional graded R-module categorifying a q-deformation of the doubly-invariant algebra ^{N^′^(w)}C[N]^N(v). In this paper, we prove that the localization C~_w,v of the category C_w,v can be obtained as the localization by right braiders arising from determinantial modules. As its application, we show several interesting properties of the localized category C~_w,v including the right rigidity.

Original language	English
Pages (from-to)	5075-5108
Number of pages	34
Journal	Mathematische Annalen
Volume	390
Issue number	4
DOIs	https://doi.org/10.1007/s00208-024-02875-z
State	Published - Dec 2024

Keywords

16D90
18M05
81R10

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title = "Localizations for quiver Hecke algebras III",

abstract = "Let R be a quiver Hecke algebra, and let Cw,v be the category of finite-dimensional graded R-module categorifying a q-deformation of the doubly-invariant algebra N′(w)C[N]N(v). In this paper, we prove that the localization C~w,v of the category Cw,v can be obtained as the localization by right braiders arising from determinantial modules. As its application, we show several interesting properties of the localized category C~w,v including the right rigidity.",

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

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. corrected publication 2024.",

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doi = "10.1007/s00208-024-02875-z",

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AU - Kashiwara, Masaki

AU - Kim, Myungho

AU - Oh, Se Jin

AU - Park, Euiyong

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024. corrected publication 2024.

PY - 2024/12

Y1 - 2024/12

N2 - Let R be a quiver Hecke algebra, and let Cw,v be the category of finite-dimensional graded R-module categorifying a q-deformation of the doubly-invariant algebra N′(w)C[N]N(v). In this paper, we prove that the localization C~w,v of the category Cw,v can be obtained as the localization by right braiders arising from determinantial modules. As its application, we show several interesting properties of the localized category C~w,v including the right rigidity.

AB - Let R be a quiver Hecke algebra, and let Cw,v be the category of finite-dimensional graded R-module categorifying a q-deformation of the doubly-invariant algebra N′(w)C[N]N(v). In this paper, we prove that the localization C~w,v of the category Cw,v can be obtained as the localization by right braiders arising from determinantial modules. As its application, we show several interesting properties of the localized category C~w,v including the right rigidity.

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KW - 18M05

KW - 81R10

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VL - 390

SP - 5075

EP - 5108

JO - Mathematische Annalen

JF - Mathematische Annalen

IS - 4

ER -

Localizations for quiver Hecke algebras III

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