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| Bochner-Martinelli Formula for Higher Spin Operators of Several R6 Variables* |
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Citation： |
Guangzhen REN,Qianqian KANG.Bochner-Martinelli Formula for Higher Spin Operators of Several R6 Variables*[J].Chinese Annals of Mathematics B,2023,44(4):489~500 |
| Page view： 1326
Net amount： 812 |
Authors： |
Guangzhen REN; Qianqian KANG |
Foundation： |
This work was supported by the National Nature Science Foundation of China (Nos. 12101564, 11801508,11801523) and the Nature Science Foundation of Zhejiang Province (No. LY22A010013). |
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| Abstract： |
The higher spin operator of several R6 variables is an analogue of the ?-operator in theory of several complex variables. The higher spin representation of so6(C)is ⊙k C4 and the higher spin operator Dk acts on ⊙k C4-valued functions. In this paper, the authors establish the Bochner-Martinelli formula for higher spin operator Dk of several R6 variables. The embedding of R6n into the space of complex 4n × 4 matrices allows them to use two-component notation, which makes the spinor calculus on R6n more concrete and explicit. A function annihilated by Dk is called k-monogenic. They give the Penrose integral formula over R6n and construct many k-monogenic polynomials. |
Keywords： |
Higher spin operator, k-Monogenic, Bochner-Martinelli formula, Penrose integral formula |
Classification： |
32A25, 32W05 |
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