On Ext-transfer for Reductive Lie Algebras

Yi Yang Li; Bin Shu; Yu Feng Yao

doi:10.1007/s10468-015-9558-3

On Ext-transfer for Reductive Lie Algebras

Yi Yang Li^*
, Bin Shu
, Yu Feng Yao

^*Corresponding author for this work

School of Mathematical Sciences

Shanghai University of Engineering Science
Shanghai Maritime University

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

1 Scopus citations

Abstract

Let G be a connected reductive algebraic group over an algebraically closed field of prime characteristic p and g be the Lie algebra of G. In this paper, we study the representations of g when p-character has standard Levi form. An Ext-transfer from the Ext-groups of induced g-modules to its Levi subalgebras is obtained. Furthermore, we reduce the computation of the multiplicities of simple factors in baby Verma modules over g to its Levi subalgebras.

Original language	English
Pages (from-to)	7-16
Number of pages	10
Journal	Algebras and Representation Theory
Volume	19
Issue number	1
DOIs	https://doi.org/10.1007/s10468-015-9558-3
State	Published - 1 Feb 2016

Keywords

Baby Verma module
Ext-transfer
Extension group
Induced module
Standard Levi form

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title = "On Ext-transfer for Reductive Lie Algebras",

abstract = "Let G be a connected reductive algebraic group over an algebraically closed field of prime characteristic p and g be the Lie algebra of G. In this paper, we study the representations of g when p-character has standard Levi form. An Ext-transfer from the Ext-groups of induced g-modules to its Levi subalgebras is obtained. Furthermore, we reduce the computation of the multiplicities of simple factors in baby Verma modules over g to its Levi subalgebras.",

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N2 - Let G be a connected reductive algebraic group over an algebraically closed field of prime characteristic p and g be the Lie algebra of G. In this paper, we study the representations of g when p-character has standard Levi form. An Ext-transfer from the Ext-groups of induced g-modules to its Levi subalgebras is obtained. Furthermore, we reduce the computation of the multiplicities of simple factors in baby Verma modules over g to its Levi subalgebras.

AB - Let G be a connected reductive algebraic group over an algebraically closed field of prime characteristic p and g be the Lie algebra of G. In this paper, we study the representations of g when p-character has standard Levi form. An Ext-transfer from the Ext-groups of induced g-modules to its Levi subalgebras is obtained. Furthermore, we reduce the computation of the multiplicities of simple factors in baby Verma modules over g to its Levi subalgebras.

KW - Baby Verma module

KW - Ext-transfer

KW - Extension group

KW - Induced module

KW - Standard Levi form

UR - https://www.scopus.com/pages/publications/84959303849

U2 - 10.1007/s10468-015-9558-3

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IS - 1

ER -

On Ext-transfer for Reductive Lie Algebras

Abstract

Keywords

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