题  目:：Penrose transformation and  k-Cauchy-Fueter operators in quaternion analysis

报告人：王伟 教授     浙江大学数学系

时  间：5月3日星期四下午4：30--5：30 

地  点：管研楼1518

摘  要：By using complex geometric method associated to the Penrose transformation, we can obtain an exact sequence over the complex space, whose associated differential complex over quaternionic space is the k-Cauchy-Fueter complex. By solving this differential complex, we can derive many properties of k-regular functions, e.g., Hartogs' extension phenomenon. The construction also implies the following 1-1 correspondence: the first cohomology group of the sheaf O (-k-2) over the projective space and the solutions to the k-Cauchy-Fueter equations on the quaternionic space. According to the realization of the first cohomology as closed (0, 1)-forms or Cech cochains, we can realize this correspondence as two integral transformations.  

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