Simple bounded highest weight modules of basic classical Lie superalgebras

Maria Gorelik; Dimitar Grantcharov

doi:10.1007/s00031-020-09616-x

Simple bounded highest weight modules of basic classical Lie superalgebras

Maria Gorelik, Dimitar Grantcharov

Department of Mathematics

Weizmann Institute of Science

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

Abstract

We classify all simple bounded highest weight modules of a basic classical Lie superalgebra g. In particular, our result leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of g.

Original language	English
Pages (from-to)	893-914
Number of pages	22
Journal	Transformation Groups
Volume	26
Issue number	3
DOIs	https://doi.org/10.1007/s00031-020-09616-x
State	Published - Sep 2021

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Geometry and Topology

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10.1007/s00031-020-09616-x

https://arxiv.org/abs/1812.11593License: Other

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title = "Simple bounded highest weight modules of basic classical Lie superalgebras",

abstract = "We classify all simple bounded highest weight modules of a basic classical Lie superalgebra g. In particular, our result leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of g.",

author = "Maria Gorelik and Dimitar Grantcharov",

note = "We are grateful to A. Joseph, I. Penkov, and V. Serganova for the helpful discussions and the referees for the useful remarks and suggestions. We also acknowledge the hospitality and excellent working conditions at the Weizmann Institute of Science and the University of Texas at Arlington where parts of this work were completed. Maria Gorelik is supported in part by the Minerva foundation with funding from the Federal German Ministry for Education and Research. Dimitar Grantcharov is supported in part by Simons Collaboration Grant 358245.",

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doi = "10.1007/s00031-020-09616-x",

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AU - Grantcharov, Dimitar

N1 - We are grateful to A. Joseph, I. Penkov, and V. Serganova for the helpful discussions and the referees for the useful remarks and suggestions. We also acknowledge the hospitality and excellent working conditions at the Weizmann Institute of Science and the University of Texas at Arlington where parts of this work were completed. Maria Gorelik is supported in part by the Minerva foundation with funding from the Federal German Ministry for Education and Research. Dimitar Grantcharov is supported in part by Simons Collaboration Grant 358245.

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N2 - We classify all simple bounded highest weight modules of a basic classical Lie superalgebra g. In particular, our result leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of g.

AB - We classify all simple bounded highest weight modules of a basic classical Lie superalgebra g. In particular, our result leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of g.

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DO - 10.1007/s00031-020-09616-x

M3 - مقالة

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JO - Transformation Groups

JF - Transformation Groups

IS - 3

ER -

Simple bounded highest weight modules of basic classical Lie superalgebras

Abstract

All Science Journal Classification (ASJC) codes

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