Supercategorification of quantum Kac-Moody algebras II

Seok Jin Kang; Masaki Kashiwara; Se jin Oh

doi:10.1016/j.aim.2014.07.036

Supercategorification of quantum Kac-Moody algebras II

Seok Jin Kang, Masaki Kashiwara, Se jin Oh

Department of Mathematics

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

18 Scopus citations

Abstract

In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family of quantum superalgebras and their integrable highest weight modules. We show that, by taking a specialization, we obtain a supercategorification of quantum Kac-Moody superalgebras and their integrable highest weight modules.

Original language	English
Pages (from-to)	169-240
Number of pages	72
Journal	Advances in Mathematics
Volume	265
DOIs	https://doi.org/10.1016/j.aim.2014.07.036
State	Published - 10 Nov 2014

Keywords

Categorification
Cyclotomic quotient
Quantum Kac-Moody superalgebras
Quiver Hecke superalgebras

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abstract = "In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family of quantum superalgebras and their integrable highest weight modules. We show that, by taking a specialization, we obtain a supercategorification of quantum Kac-Moody superalgebras and their integrable highest weight modules.",

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AB - In this paper, we investigate the supercategories consisting of supermodules over quiver Hecke superalgebras and cyclotomic quiver Hecke superalgebras. We prove that these supercategories provide a supercategorification of a certain family of quantum superalgebras and their integrable highest weight modules. We show that, by taking a specialization, we obtain a supercategorification of quantum Kac-Moody superalgebras and their integrable highest weight modules.

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KW - Cyclotomic quotient

KW - Quantum Kac-Moody superalgebras

KW - Quiver Hecke superalgebras

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JO - Advances in Mathematics

JF - Advances in Mathematics

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Supercategorification of quantum Kac-Moody algebras II

Abstract

Keywords

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