The tangential \(k\)-Cauchy-Fueter complexes and Hartogs’ phenomenon over the right quaternionic Heisenberg group. (English) Zbl 1447.58022
The authors construct the tangential \(k\)-Cauchy-Fueter complexes on the right quaternionic Heisenberg group, as the quaternionic counterpart of \(\bar{\partial} _b\)-complex on the Heisenberg group in the theory of several complex variables. They use the \(L^2\) estimate to solve the nonhomogeneous tangential \(k\)-Cauchy-Fueter equation under the compatibility condition over this group modulo a lattice. This solution has an important vanishing property when the group is higher dimensional. It allows to prove the Hartogs’ extension phenomenon for \(k\)-CF functions, which are the quaternionic counterpart of CR functions.
Reviewer: Mehdi Rafie-Rad (Babolsar)
MSC:
| 58J10 | Differential complexes |
| 35N15 | \(\overline\partial\)-Neumann problems and formal complexes in context of PDEs |
| 35R03 | PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. |
| 30C35 | General theory of conformal mappings |
| 81R05 | Finite-dimensional groups and algebras motivated by physics and their representations |
Keywords:
tangential \(k\)-Cauchy-Fueter complex; Hartogs’ phenomenon; right quaternionic Heisenberg group; nonhomogeneous equation under compatibility condition; \(L^2\) estimateReferences:
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