Whittaker modules of the affine Kac–Moody algebra G2(1) and the <i>W</i>-algebra W(gL)

In this paper, we classify the simple nondegenerate Whittaker modules for the affine Kac–Moody Lie algebra of type G2(1). Then we handle the classification of Whittaker modules in the critical level, according to which, we discover the relationship between the W-algebra W(gL) associated with the Langlands dual algebra gL and nondegenerate Whittaker modules for ĝ of type G2(1).

Authors

Zheng Li (ORCID: https://orcid.org/0000-0001-9565-4194)
Lin Ge

Institutions

Harbin University of Science and Technology (CN)
Harbin Institute of Technology (CN)
Central China Normal University (CN)

Publication Details

Journal: Journal of Mathematical Physics
Published: 2025-09-01
DOI: https://doi.org/10.1063/5.0250229
Primary Topic: Algebraic structures and combinatorial models
Type: article
Field-Weighted Citation Impact: 0.00

Funders

National Natural Science Foundation of China
China Postdoctoral Science Foundation
National Postdoctoral Program for Innovative Talents

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article

Whittaker modules of the affine Kac–Moody algebra G2(1) and the W-algebra W(gL)

Zheng Li, Lin Ge

Sep 1, 2025

Journal of Mathematical Physics

Algebraic structures and combinatorial models

article

Whittaker modules of the affine Kac–Moody algebra G2(1) and the W-algebra W(gL)

Zheng Li, Lin Ge

September 1, 2025article en

Abstract

In this paper, we classify the simple nondegenerate Whittaker modules for the affine Kac–Moody Lie algebra of type G2(1). Then we handle the classification of Whittaker modules in the critical level, according to which, we discover the relationship between the W-algebra W(gL) associated with the Langlands dual algebra gL and nondegenerate Whittaker modules for ĝ of type G2(1).

Journal of Mathematical PhysicsVol. 66(9)

Harbin University of Science and Technology (CN), Harbin Institute of Technology (CN), Central China Normal University (CN)

National Natural Science Foundation of China, China Postdoctoral Science Foundation, National Postdoctoral Program for Innovative Talents

Openalex Percentile: Top 71%

Algebraic structures and combinatorial models

DOI Source OpenAlex

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