Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Duality and monodromy reducibility of $A$-hypergeometric systems   We study $A$-hypergeometric systems $H_A(\beta)$ in the sense of Gelfand,
Kapranov and Zelevinsky under two aspects: the structure of their holonomically
dual system, and reducibility of their rank module.
  We prove first that rank-jumping parameters always correspond to reducible
systems, and we show that the property of being reducible is ``invariant modulo
the lattice''. In the second part we study a conjecture of Nobuki Takayama
which states that the holonomic dual of $H_A(\beta)$ is of the form
$H_A(\beta')$ for suitable $\beta'$. We prove the conjecture for all matrices
$A$ and generic parameter $\beta$, exhibit an example that shows that in
general the conjecture cannot hold, and present a refined version of the
conjecture.
  Questions on both duality and reducibility have been impossible to answer
with classical methods. This paper may be seen as an example of the usefulness,
and scope of applications, of the homological tools for $A$-hypergeometric
systems developed in \cite{MMW}.

37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th