摘要
In this paper,we study irreducible non-weight modules over the mirror Heisenberg-Virasoro algebra D,including Whittaker modules,U(Cd_(0))-free modules and their tensor products.More precisely,we give the necessary and sufficient conditions for the Whittaker modules to be irreducible.We determine all the D-module structures on U(Cd_(0)),and find the necessary and sufficient conditions for these modules to be irreducible.At last,we determine the necessary and sufficient conditions for the tensor products of Whittaker modules and U(Cd_(0))-free modules to be irreducible,and obtain that any two such tensor products are isomorphic if and only if the corresponding Whittaker modules and U(Cd_(0))-free modules are isomorphic.These lead to many new irreducible non-weight modules over D.
基金
supported by China Scholarship Council(Grant No.201906340096)
National Natural Science Foundation of China(Grant Nos.11771410 and 11931009)
supported by National Natural Science Foundation of China(Grant No.11801066)
supported by National Natural Science Foundation of China(Grant No.11871190)
Natural Sciences and Engineering Research Council of Canada(Grant No.311907-2020).
