Perfect bases for integrable modules over generalized Kac-Moody algebras

Seok Jin Kang; Se Jin Oh; Euiyong Park

doi:10.1007/s10468-009-9204-z

Perfect bases for integrable modules over generalized Kac-Moody algebras

Seok Jin Kang, Se Jin Oh, Euiyong Park

Department of Mathematics

Seoul National University

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

11 Scopus citations

Abstract

We introduce the notion of perfect bases for integrable highest weight modules over generalized Kac-Moody algebras and show that the colored oriented graphs arising from perfect bases are isomorphic to the highest weight crystals B(λ) over quantum generalized Kac-Moody algebras.

Original language	English
Pages (from-to)	571-587
Number of pages	17
Journal	Algebras and Representation Theory
Volume	14
Issue number	3
DOIs	https://doi.org/10.1007/s10468-009-9204-z
State	Published - Jun 2011

Keywords

Crystal bases
Generalized Kac-Moody algebras
Perfect bases
Representations

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title = "Perfect bases for integrable modules over generalized Kac-Moody algebras",

abstract = "We introduce the notion of perfect bases for integrable highest weight modules over generalized Kac-Moody algebras and show that the colored oriented graphs arising from perfect bases are isomorphic to the highest weight crystals B(λ) over quantum generalized Kac-Moody algebras.",

keywords = "Crystal bases, Generalized Kac-Moody algebras, Perfect bases, Representations",

author = "Kang, {Seok Jin} and Oh, {Se Jin} and Euiyong Park",

year = "2011",

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AU - Oh, Se Jin

AU - Park, Euiyong

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N2 - We introduce the notion of perfect bases for integrable highest weight modules over generalized Kac-Moody algebras and show that the colored oriented graphs arising from perfect bases are isomorphic to the highest weight crystals B(λ) over quantum generalized Kac-Moody algebras.

AB - We introduce the notion of perfect bases for integrable highest weight modules over generalized Kac-Moody algebras and show that the colored oriented graphs arising from perfect bases are isomorphic to the highest weight crystals B(λ) over quantum generalized Kac-Moody algebras.

KW - Crystal bases

KW - Generalized Kac-Moody algebras

KW - Perfect bases

KW - Representations

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U2 - 10.1007/s10468-009-9204-z

DO - 10.1007/s10468-009-9204-z

M3 - Article

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EP - 587

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

IS - 3

ER -

Perfect bases for integrable modules over generalized Kac-Moody algebras

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Keywords

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