Supercategorification of quantum Kac-Moody algebras

Seok Jin Kang; Masaki Kashiwara; Se jin Oh

doi:10.1016/j.aim.2013.04.008

Supercategorification of quantum Kac-Moody algebras

Seok Jin Kang, Masaki Kashiwara, Se jin Oh

Department of Mathematics

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

19 Scopus citations

Abstract

We show that the quiver Hecke superalgebras and their cyclotomic quotients provide a supercategorification of quantum Kac-Moody algebras and their integrable highest weight modules.

Original language	English
Pages (from-to)	116-162
Number of pages	47
Journal	Advances in Mathematics
Volume	242
DOIs	https://doi.org/10.1016/j.aim.2013.04.008
State	Published - 1 Aug 2013

Bibliographical note

Funding Information:
The first author’s work was supported by NRF Grant # 2012-005700 and NRF Grant # 2011-0027952 . The second author’s work was supported by Grant-in-Aid for Scientific Research (B) 22340005 , Japan Society for the Promotion of Science . The third author’s work was supported by BK21 Mathematical Sciences Division and NRF Grant # 2012-005700 .

Keywords

Categorification
Cyclotomic quotients
Quantum Kac-Moody algebras
Quiver Hecke superalgebras

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10.1016/j.aim.2013.04.008

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title = "Supercategorification of quantum Kac-Moody algebras",

abstract = "We show that the quiver Hecke superalgebras and their cyclotomic quotients provide a supercategorification of quantum Kac-Moody algebras and their integrable highest weight modules.",

keywords = "Categorification, Cyclotomic quotients, Quantum Kac-Moody algebras, Quiver Hecke superalgebras",

author = "Kang, {Seok Jin} and Masaki Kashiwara and Oh, {Se jin}",

note = "Funding Information: The first author{\textquoteright}s work was supported by NRF Grant # 2012-005700 and NRF Grant # 2011-0027952 . The second author{\textquoteright}s work was supported by Grant-in-Aid for Scientific Research (B) 22340005 , Japan Society for the Promotion of Science . The third author{\textquoteright}s work was supported by BK21 Mathematical Sciences Division and NRF Grant # 2012-005700 .",

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doi = "10.1016/j.aim.2013.04.008",

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journal = "Advances in Mathematics",

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AU - Kashiwara, Masaki

AU - Oh, Se jin

N1 - Funding Information: The first author’s work was supported by NRF Grant # 2012-005700 and NRF Grant # 2011-0027952 . The second author’s work was supported by Grant-in-Aid for Scientific Research (B) 22340005 , Japan Society for the Promotion of Science . The third author’s work was supported by BK21 Mathematical Sciences Division and NRF Grant # 2012-005700 .

PY - 2013/8/1

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N2 - We show that the quiver Hecke superalgebras and their cyclotomic quotients provide a supercategorification of quantum Kac-Moody algebras and their integrable highest weight modules.

AB - We show that the quiver Hecke superalgebras and their cyclotomic quotients provide a supercategorification of quantum Kac-Moody algebras and their integrable highest weight modules.

KW - Categorification

KW - Cyclotomic quotients

KW - Quantum Kac-Moody algebras

KW - Quiver Hecke superalgebras

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DO - 10.1016/j.aim.2013.04.008

M3 - Article

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SN - 0001-8708

VL - 242

SP - 116

EP - 162

JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Supercategorification of quantum Kac-Moody algebras

Abstract

Bibliographical note

Keywords

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