Inhaltsangabeand summary of results.- Elliptic genera.- Vertex operator super algebras.- G-invariant vertex operator super subalgebras.- Geometric structure in vector spaces and reduction of structure groups on manifolds.- Infinite dimensional symmetries in elliptic genera for Kähler manifolds.

Introduction and summary of results.- Elliptic genera.- Vertex Operator super-algebras.- G-invariant vertex operator super subalgebras.- Geometric structures in vector spaces and structure groups on manifolds.- Infinite dimensional symmetries in elliptic genera for Kähler manifolds.

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