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Classification of gradient space of dimension 8 by a reducible sℓ(2, C) action

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Abstract

This paper deals with a reducible sℓ(2,C) action on the formal power series ring. The purpose of this paper is to confirm a special case of the Yau conjecture: Suppose that sℓ(2,C) acts on the formal power series ring via (1.1). Then I(f) = (ℓ i1) ⊕ (ℓ i2) ⊕... ⊕ (ℓ is ) modulo some one dimensional sℓ(2,C) representations where (ℓ i ) is an irreducible sℓ(2,C) representation of ℓ i dimension and {ℓ i1 ℓ i2,...,ℓ is } ⊆ {ℓ 1 , ℓ 2...,ℓ r }. Unlike classical invariant theory which deals only with irreducible action and 1-dimensional representations, we treat the reducible action and higher dimensional representations successively.

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Authors and Affiliations

  1. Institute of Mathematics, East China Normal University, Shanghai, 200241, China

    Stephen S.-T. Yau

  2. Department of Mathematics, University of Illinois at Chicago, Chicago, IL, 60607, USA

    Stephen S.-T. Yau & HuaiQing Zuo

  3. Department of Mathematics, Cheng Kung University, Tainan, 701, Taiwan, China

    Yung Yu

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

    HuaiQing Zuo

Authors
  1. Stephen S.-T. Yau
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  2. Yung Yu
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  3. HuaiQing Zuo
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Correspondence to Stephen S.-T. Yau.

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Dedicated to Professor Zhong TongDe on the occasion of his 80th birthday

This work was supported by National Natural Science Foundation of China (Grant No. 10731030) and PSSCS of Shanghai

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Yau, S.ST., Yu, Y. & Zuo, H. Classification of gradient space of dimension 8 by a reducible sℓ(2, C) action. Sci. China Ser. A-Math. 52, 2792–2828 (2009). https://doi.org/10.1007/s11425-009-0047-1

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  • DOI: https://doi.org/10.1007/s11425-009-0047-1

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