The tangential Cauchy-Fueter complex on the quaternionic Heisenberg group

JOURNAL OF GEOMETRY AND PHYSICS

卷:61

Article

Wang, Wei

关键词: The tangential k-Cauchy-Fueter operator;    The quaternionic Heisenberg group;    Penrose transformation;    Irreducible homogeneous sheaves;    Invariant differential operators;    Representation theory;   

DOI  :  10.1016/j.geomphys.2010.10.006

来源: Elsevier

【 摘 要 】

The Cauchy-Fueter operator on the quaternionic space H-n induces the tangential Cauchy-Fueter operator on the boundary of a domain. The quaternionic Heisenberg group is a standard model of the boundaries. By using the Penrose transformation associated to a double fibration of homogeneous spaces of Sp(2N, C), we construct an exact sequence on the quaternionic Heisenberg group, the tangential k-Cauchy-Fueter complex, resolving the tangential k-Cauchy-Fueter operator Q(0)((k)) . Q(0)((1)) is the tangential Cauchy-Fueter operator. The complex gives the compatible conditions under which the non-homogeneous tangential k-Cauchy-Fueter equations Q(0)((k)) u = f are solvable. The operators in this complex are left invariant differential operators on the quaternionic Heisenberg group. This is a quaternionic version of partial derivative(b)-complex on the Heisenberg group in the theory of several complex variables. (C) 2010 Elsevier B.V. All rights reserved.

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