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

Lin Ge; Zheng Li

doi:10.1063/5.0250229

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

Lin Ge
, Zheng Li^*

^*Corresponding author for this work

Harbin Institute of Technology
Central China Normal University

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

Abstract

In this paper, we classify the simple nondegenerate Whittaker modules for the affine Kac-Moody Lie algebra of type G 2 ( 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 ( g L ) associated with the Langlands dual algebra g L and nondegenerate Whittaker modules for g ̂ of type G 2 ( 1 ) .

Original language	English
Article number	091701
Journal	Journal of Mathematical Physics
Volume	66
Issue number	9
DOIs	https://doi.org/10.1063/5.0250229
State	Published - 1 Sep 2025
Externally published	Yes

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10.1063/5.0250229

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title = "Whittaker modules of the affine Kac-Moody algebra G2(1) and the W-algebra W(gL)",

abstract = "In this paper, we classify the simple nondegenerate Whittaker modules for the affine Kac-Moody Lie algebra of type G 2 ( 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 ( g L ) associated with the Langlands dual algebra g L and nondegenerate Whittaker modules for g{\^ } of type G 2 ( 1 ) .",

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

Abstract

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