关于旋量的泊松变换

IF 0.8 Q2 MATHEMATICS
S. Ben Saïd, A. Boussejra, K. Koufany
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引用次数: 0

摘要

.设 ( τ, V τ ) 为 Spin( n ) 的一个旋量表示,设 ( σ, V σ ) 为 Spin( n - 1) 的一个旋量表示,该表示出现在限制 τ | Spin( n - 1) 中。我们认为实双曲空间 H n ( R ) 是秩一均相空间 Spin 0 (1 , n ) / Spin( n ) ,而 H n ( R ) 上的旋光束 Σ H n ( R ) 是均相束 Spin 0 (1 , n ) × Spin( n ) V τ 。我们的目的是描述作用于 Σ H n ( R ) 的不变二阶算子代数的特征特征旋子,这些特征旋子可以写成 H n ( R ) 边界 S n - 1 ≃ Spin( n ) / Spin( n - 1) 上的 Spin( n ) × Spin( n - 1) V σ 束 L p 截面的泊松变换。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On Poisson transforms for spinors
. Let ( τ, V τ ) be a spinor representation of Spin( n ) and let ( σ, V σ ) be a spinor representation of Spin( n − 1) that occurs in the restriction τ | Spin( n − 1) . We consider the real hyperbolic space H n ( R ) as the rank one homogeneous space Spin 0 (1 , n ) / Spin( n ) and the spinor bundle Σ H n ( R ) over H n ( R ) as the homogeneous bundle Spin 0 (1 , n ) × Spin( n ) V τ . Our aim is to characterize eigenspinors of the algebra of invariant differential operators acting on Σ H n ( R ) which can be written as the Poisson transform of L p -sections of the bundle Spin( n ) × Spin( n − 1) V σ over the boundary S n − 1 ≃ Spin( n ) / Spin( n − 1) of H n ( R ).
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
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