论文标题
关于从商模块获得的某种类别的均质运算符的不可约性
On irreducibility of a certain class of homogeneous operators obtained from quotient modules
论文作者
论文摘要
令$ω\ subset \ mathbb {c}^m $为一个开放，连接和边界集，$ \ mathcal {a}（ω）$是$ω$上的Holomorphic函数的函数代数。 Suppose that $\mathcal{M}_q$ is the quotient Hilbert module obtained from a submodule of functions in a Hilbert module $\mathcal{M}$ vanishing to order $k$ along a smooth irreducible complex analytic set $\mathcal{Z}\subsetΩ$ of codimension at least $2$.在本文中，我们证明了将乘法运算符压缩到$ \ Mathcal {m} _q $上是同质的，这对于自动形态组的适当亚组aut $（ω）$ $ω$的$ g $ g $ g $ g $ g $ g $ g ot aut $（ω）$ aut $（ω）$ abor ythe $ nive ythe $ abor ythe $ \ ytherications $ \ ytherications $ \ ytherications $ \ yatherage $ \ ytherications $ \ ytheriogational ytherig ythe y themog at ythemog af yath $ c。 $ g $和$ \ MATHCAL {M} $以及$ \ Mathcal {M} _Q $在Cowen-Douglas类中。我们表明，即使在$ \ Mathcal {M} $上的乘法元素的元组是不可约束的，即使乘法运算符的元组是不可记录的，乘以乘法运算符的这些压缩也可能是可还原的。此外，这些可还原的运营商的不可还原组件被确定为通用的威尔金斯运营商。
Let $ Ω\subset \mathbb{C}^m $ be an open, connected and bounded set and $\mathcal{A}(Ω)$ be a function algebra of holomorphic functions on $Ω$. Suppose that $\mathcal{M}_q$ is the quotient Hilbert module obtained from a submodule of functions in a Hilbert module $\mathcal{M}$ vanishing to order $k$ along a smooth irreducible complex analytic set $\mathcal{Z}\subsetΩ$ of codimension at least $2$. In this article, we prove that the compression of the multiplication operators onto $\mathcal{M}_q$ is homogeneous with respect to a suitable subgroup of the automorphism group Aut$(Ω)$ of $Ω$ depending upon a subgroup $G$ of Aut$(Ω)$ whenever the tuple of multiplication operators on $\mathcal{M}$ is homogeneous with respect to $G$ and both $\mathcal{M}$ as well as $\mathcal{M}_q$ are in the Cowen-Douglas class. We show that these compression of multiplication operators might be reducible even if the tuple of multiplication operators on $\mathcal{M}$ is irreducible by exhibiting a concrete example. Moreover, the irreducible components of these reducible operators are identified as Generalized Wilkins' operators.
