Categorification of highest weight modules over quantum generalized Kac-Moody algebras

Seok Jin Kang; Masaki Kashiwara; Se Jin Oh

doi:10.17323/1609-4514-2013-13-2-315-343

Categorification of highest weight modules over quantum generalized Kac-Moody algebras

Seok Jin Kang, Masaki Kashiwara, Se Jin Oh

Department of Mathematics

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

5 Scopus citations

Abstract

Let U_q (g) be a quantum generalized Kac-Moody algebra and let V (Λ) be the integrable highest weight U_q (g)-module with highest weight Λ. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra R^Λ provides a categorification of V (Λ).

Original language	English
Pages (from-to)	315-343
Number of pages	29
Journal	Moscow Mathematical Journal
Volume	13
Issue number	2
DOIs	https://doi.org/10.17323/1609-4514-2013-13-2-315-343
State	Published - 2013

Keywords

Categorification
Cyclotomic quotient
Khovanov-lauda-rouquier algebras
Quantum generalized Kac-Moody algebras

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10.17323/1609-4514-2013-13-2-315-343

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title = "Categorification of highest weight modules over quantum generalized Kac-Moody algebras",

abstract = "Let Uq (g) be a quantum generalized Kac-Moody algebra and let V (Λ) be the integrable highest weight Uq (g)-module with highest weight Λ. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra RΛ provides a categorification of V (Λ).",

keywords = "Categorification, Cyclotomic quotient, Khovanov-lauda-rouquier algebras, Quantum generalized Kac-Moody algebras",

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

year = "2013",

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volume = "13",

pages = "315--343",

journal = "Moscow Mathematical Journal",

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publisher = "Independent University of Moscow",

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AU - Kang, Seok Jin

AU - Kashiwara, Masaki

AU - Oh, Se Jin

PY - 2013

Y1 - 2013

N2 - Let Uq (g) be a quantum generalized Kac-Moody algebra and let V (Λ) be the integrable highest weight Uq (g)-module with highest weight Λ. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra RΛ provides a categorification of V (Λ).

AB - Let Uq (g) be a quantum generalized Kac-Moody algebra and let V (Λ) be the integrable highest weight Uq (g)-module with highest weight Λ. We prove that the cyclotomic Khovanov-Lauda-Rouquier algebra RΛ provides a categorification of V (Λ).

KW - Categorification

KW - Cyclotomic quotient

KW - Khovanov-lauda-rouquier algebras

KW - Quantum generalized Kac-Moody algebras

UR - https://www.scopus.com/pages/publications/84875601110

U2 - 10.17323/1609-4514-2013-13-2-315-343

DO - 10.17323/1609-4514-2013-13-2-315-343

M3 - Article

AN - SCOPUS:84875601110

SN - 1609-3321

VL - 13

SP - 315

EP - 343

JO - Moscow Mathematical Journal

JF - Moscow Mathematical Journal

IS - 2

ER -

Categorification of highest weight modules over quantum generalized Kac-Moody algebras

Abstract

Keywords

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