Classical Whittaker modules for the classical affine Kac-Moody algebras

Lin Ge; Zheng Li

doi:10.1016/j.jalgebra.2023.12.036

Classical Whittaker modules for the classical affine Kac-Moody algebras

Lin Ge
, Zheng Li^*

^*Corresponding author for this work

University of Science and Technology of China

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

4 Scopus citations

Abstract

Inspired by Sugawara operators, we introduce a new basis for the universal non-degenerate Whittaker module of level κ over the classical affine Kac-Moody algebra of type B_N⁽¹⁾, C_N⁽¹⁾ or D_N⁽¹⁾. This basis is different from the one derived from the PBW basis and would help us to understand the structure of Whittaker modules. As a result, we classify simple non-degenerate Whittaker modules for the classical affine Kac-Moody algebras whether at the critical or noncritical level.

Original language	English
Pages (from-to)	23-63
Number of pages	41
Journal	Journal of Algebra
Volume	644
DOIs	https://doi.org/10.1016/j.jalgebra.2023.12.036
State	Published - 15 Apr 2024
Externally published	Yes

Keywords

Affine Kac-Moody algebras
Simple modules
Sugawara operators
Whittaker modules

Access to Document

10.1016/j.jalgebra.2023.12.036

Cite this

@article{6c8115de22004d988ca3ecda2ae2397a,

title = "Classical Whittaker modules for the classical affine Kac-Moody algebras",

abstract = "Inspired by Sugawara operators, we introduce a new basis for the universal non-degenerate Whittaker module of level κ over the classical affine Kac-Moody algebra of type BN(1), CN(1) or DN(1). This basis is different from the one derived from the PBW basis and would help us to understand the structure of Whittaker modules. As a result, we classify simple non-degenerate Whittaker modules for the classical affine Kac-Moody algebras whether at the critical or noncritical level.",

keywords = "Affine Kac-Moody algebras, Simple modules, Sugawara operators, Whittaker modules",

author = "Lin Ge and Zheng Li",

note = "Publisher Copyright: {\textcopyright} 2024 Elsevier Inc.",

year = "2024",

month = apr,

day = "15",

doi = "10.1016/j.jalgebra.2023.12.036",

language = "英语",

volume = "644",

pages = "23--63",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Classical Whittaker modules for the classical affine Kac-Moody algebras

AU - Ge, Lin

AU - Li, Zheng

PY - 2024/4/15

Y1 - 2024/4/15

N2 - Inspired by Sugawara operators, we introduce a new basis for the universal non-degenerate Whittaker module of level κ over the classical affine Kac-Moody algebra of type BN(1), CN(1) or DN(1). This basis is different from the one derived from the PBW basis and would help us to understand the structure of Whittaker modules. As a result, we classify simple non-degenerate Whittaker modules for the classical affine Kac-Moody algebras whether at the critical or noncritical level.

AB - Inspired by Sugawara operators, we introduce a new basis for the universal non-degenerate Whittaker module of level κ over the classical affine Kac-Moody algebra of type BN(1), CN(1) or DN(1). This basis is different from the one derived from the PBW basis and would help us to understand the structure of Whittaker modules. As a result, we classify simple non-degenerate Whittaker modules for the classical affine Kac-Moody algebras whether at the critical or noncritical level.

KW - Affine Kac-Moody algebras

KW - Simple modules

KW - Sugawara operators

KW - Whittaker modules

UR - https://www.scopus.com/pages/publications/85183526188

U2 - 10.1016/j.jalgebra.2023.12.036

DO - 10.1016/j.jalgebra.2023.12.036

M3 - 文章

AN - SCOPUS:85183526188

SN - 0021-8693

VL - 644

SP - 23

EP - 63

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Classical Whittaker modules for the classical affine Kac-Moody algebras

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this