ASSOCIATED VARIETIES OF MINIMAL HIGHEST WEIGHT MODULES

Zhanqiang Bai; Jia Jun Ma; Wei Xiao; Xun Xie

doi:10.1090/ert/681

ASSOCIATED VARIETIES OF MINIMAL HIGHEST WEIGHT MODULES

Zhanqiang Bai, Jia Jun Ma, Wei Xiao, Xun Xie

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

1 Scopus citations

Abstract

Let g be a complex simple Lie algebra. A simple g-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit. The main result of this paper is a classification of minimal highest weight modules for g. This classification extends the work of Joseph [Ann. Sci. École Norm. Sup. (4) 31 (1998), 17–45], which focused on categorizing minimal highest weight modules annihilated by completely prime ideals. Furthermore, we have determined the associated varieties of these modules. In other words, we have identified all possible weak quantizations of minimal orbital varieties.

Original language	English
Pages (from-to)	498-513
Number of pages	16
Journal	Representation Theory
Volume	28
DOIs	https://doi.org/10.1090/ert/681
State	Published - 1 Jan 2024
Externally published	Yes

Keywords

Associated variety
Gelfand–Kirillov dimension
Kazhdan-Lusztig cell
minimal orbit
orbital variety

ASJC Scopus subject areas

Mathematics (miscellaneous)

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title = "ASSOCIATED VARIETIES OF MINIMAL HIGHEST WEIGHT MODULES",

abstract = "Let g be a complex simple Lie algebra. A simple g-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit. The main result of this paper is a classification of minimal highest weight modules for g. This classification extends the work of Joseph [Ann. Sci. {\'E}cole Norm. Sup. (4) 31 (1998), 17–45], which focused on categorizing minimal highest weight modules annihilated by completely prime ideals. Furthermore, we have determined the associated varieties of these modules. In other words, we have identified all possible weak quantizations of minimal orbital varieties.",

keywords = "Associated variety, Gelfand–Kirillov dimension, Kazhdan-Lusztig cell, minimal orbit, orbital variety",

author = "Zhanqiang Bai and Ma, {Jia Jun} and Wei Xiao and Xun Xie",

note = "Publisher Copyright: {\textcopyright} 2024 American Mathematical Society",

year = "2024",

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doi = "10.1090/ert/681",

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AU - Bai, Zhanqiang

AU - Ma, Jia Jun

AU - Xiao, Wei

AU - Xie, Xun

PY - 2024/1/1

Y1 - 2024/1/1

N2 - Let g be a complex simple Lie algebra. A simple g-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit. The main result of this paper is a classification of minimal highest weight modules for g. This classification extends the work of Joseph [Ann. Sci. École Norm. Sup. (4) 31 (1998), 17–45], which focused on categorizing minimal highest weight modules annihilated by completely prime ideals. Furthermore, we have determined the associated varieties of these modules. In other words, we have identified all possible weak quantizations of minimal orbital varieties.

AB - Let g be a complex simple Lie algebra. A simple g-module is called minimal if the associated variety of its annihilator ideal coincides with the closure of the minimal nilpotent coadjoint orbit. The main result of this paper is a classification of minimal highest weight modules for g. This classification extends the work of Joseph [Ann. Sci. École Norm. Sup. (4) 31 (1998), 17–45], which focused on categorizing minimal highest weight modules annihilated by completely prime ideals. Furthermore, we have determined the associated varieties of these modules. In other words, we have identified all possible weak quantizations of minimal orbital varieties.

KW - Associated variety

KW - Gelfand–Kirillov dimension

KW - Kazhdan-Lusztig cell

KW - minimal orbit

KW - orbital variety

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JO - Representation Theory

JF - Representation Theory

ER -

ASSOCIATED VARIETIES OF MINIMAL HIGHEST WEIGHT MODULES

Abstract

Keywords

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