A recursive basis for primitive forms in symplectic spaces and applications to Heisenberg groups

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• 作者：Annalisa Baldi ; Marilena Barnabei ; Bruno Franchi
• 关键词：Symplectic manifolds ; differential forms ; Heisenberg groups ; combinatorial functions ; 53D05 ; 58A10 ; 43A80 ; 05A10
• 刊名：Acta Mathematica Sinica
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：32
• 期：3
• 页码：265-285
• 全文大小：302 KB
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  [13]Rumin, M.: Around heat decay on forms and relations of nilpotent Lie groups. In: Séminaire de Théorie Spectrale et Géométrie, Vol. 19, Année 2000–2001, of Sémin. Théor. Spectr. Géom., Univ. Grenoble I, 2001, 123–164MathSciNet
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• 作者单位：Annalisa Baldi (1)
  Marilena Barnabei (1)
  Bruno Franchi (1)
  
  1. Dipartimento di Matematica, Piazza di Porta S. Donato 5, 40126, Bologna, Italy
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617

文摘

This paper is divided in two parts: in Section 2, we define recursively a privileged basis of the primitive forms in a symplectic space (V 2n , ω). Successively, in Section 3, we apply our construction in the setting of Heisenberg groups ℍ ^{n , n ≥ 1, to write in coordinates the exterior differential of the so-called Rumin’s complex of differential forms in ℍ n . Keywords Symplectic manifolds differential forms Heisenberg groups combinatorial functions}