Grassmanniennes de dimension infinie, groupes de lacets et opérateur vertex

Abstract : In the first part of this work, we studied the infinite dimensional Grassmannians of a separable Hilbert space. More exactly, the link between hilbertian grassmannians and its connected components, the restricted general linear group, and the open sets covering of this hilbertian grassmannian. We studied also the connected components of a dense grassmannian of a hilbertian grassmannian, the link between its connected components and its cellular Schubert decomposition. At the end of this part, we show the topologic relation existing between the infinite dimensional grassmannians and the finite dimensional once. In the second part of this work, we studied the link between the loop groups and the grassmannians, we studied also the operator vertex's action on the grassmannian's elements associated to the tau function
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Abdelhay Semlali. Grassmanniennes de dimension infinie, groupes de lacets et opérateur vertex. Mathématiques générales [math.GM]. Université Paul Verlaine - Metz, 1996. Français. ⟨NNT : 1996METZ046S⟩. ⟨tel-01777159⟩

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