Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On irreducibility of a certain class of homogeneous operators obtained
  from quotient modules   Let $ \Omega \subset \mathbb{C}^m $ be an open, connected and bounded set and
$\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on
$\Omega$. 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
$\mathcal{Z}\subset\Omega$ 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$(\Omega)$ of $\Omega$ depending upon a subgroup $G$ of Aut$(\Omega)$
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.

28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
7
The categories of this paper are: hep-th