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On Ext-transfer for Reductive Lie Algebras

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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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Authors and Affiliations

  1. School of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201620, China

    Yi-Yang Li

  2. Department of Mathematics, East China Normal University, Shanghai, 200241, China

    Bin Shu

  3. Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, China

    Yu-Feng Yao

Authors
  1. Yi-Yang Li
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  2. Bin Shu
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  3. Yu-Feng Yao
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Corresponding author

Correspondence to Yi-Yang Li.

Additional information

Presented by Jon F. Carlson.

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11201293 and 11271130) and the Innovation Program of Shanghai Municipal Education Commission (Grant Nos. 12ZZ038 and 13YZ077). The authors thank the referee of this paper deeply for providing very useful comments.

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Li, YY., Shu, B. & Yao, YF. On Ext-transfer for Reductive Lie Algebras. Algebr Represent Theor 19, 7–16 (2016). https://doi.org/10.1007/s10468-015-9558-3

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  • DOI: https://doi.org/10.1007/s10468-015-9558-3

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