Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dual pairs in the Pin-group and duality for the corresponding spinorial
  representation   In this paper, we give a complete picture of Howe correspondence for the
setting ($O(E, b), Pin(E, b), \Pi$), where $O(E, b)$ is an orthogonal group
(real or complex), $Pin(E, b)$ is the two-fold Pin-covering of $O(E, b)$, and
$\Pi$ is the spinorial representation of $Pin(E, b)$. More precisely, for a
dual pair ($G, G'$) in $O(E, b)$, we determine explicitly the nature of its
preimages $(\tilde{G}, \tilde{G'})$ in $Pin(E, b)$, and prove that apart from
some exceptions, $(\tilde{G}, \tilde{G'})$ is always a dual pair in $Pin(E,
b)$; then we establish the Howe correspondence for $\Pi$ with respect to
$(\tilde{G}, \tilde{G'})$.

15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an