In this paper,we study the tensor module P■M over the Witt superalgebra W_(m,n)~+(resp.W_(m,n)),where P is a simple module over the Weyl superalgebra K_(m,n)~+(resp.K_(m,n))and M is a simple weight module over the ge...In this paper,we study the tensor module P■M over the Witt superalgebra W_(m,n)~+(resp.W_(m,n)),where P is a simple module over the Weyl superalgebra K_(m,n)~+(resp.K_(m,n))and M is a simple weight module over the general linear Lie superalgebra gl(m,n).We obtain the necessary and sufficient conditions for P■M to be simple,and determine all the simple subquotients of P■M when it is not simple.All the work leads to the completion of some classification problems on the weight representation theories of W_(m,n)~+and W_(m,n).展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11971440,11801390 and 11871052)。
文摘In this paper,we study the tensor module P■M over the Witt superalgebra W_(m,n)~+(resp.W_(m,n)),where P is a simple module over the Weyl superalgebra K_(m,n)~+(resp.K_(m,n))and M is a simple weight module over the general linear Lie superalgebra gl(m,n).We obtain the necessary and sufficient conditions for P■M to be simple,and determine all the simple subquotients of P■M when it is not simple.All the work leads to the completion of some classification problems on the weight representation theories of W_(m,n)~+and W_(m,n).
