In this paper we define tensor modules （sheaves） of Schur type and of generalized Schur type associated with given modules （sheaves）, using the so-called Schur functors. According to the functorial property, we gi...In this paper we define tensor modules （sheaves） of Schur type and of generalized Schur type associated with given modules （sheaves）, using the so-called Schur functors. According to the functorial property, we give a series of tensor modules （sheaves） of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules （sheaves） of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.展开更多
文摘In this paper we define tensor modules （sheaves） of Schur type and of generalized Schur type associated with given modules （sheaves）, using the so-called Schur functors. According to the functorial property, we give a series of tensor modules （sheaves） of Schur types in a categorical description. The main conclusion is that, by using basic ideas of algebraic geometry, there exists a canonical isomorphism of different tensor modules （sheaves） of Schur types if the original sheaf is locally free, which is in fact a generalization of results in linear algebra into locally free sheaves.
