Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zak transform, Weil representation, and integral operators with
  theta-kernels   The Weil representation of a real symplectic group $Sp(2n,R)$ admits a
canonical extension to a holomorphic representation of a certain complex
semigroup consisting of Lagrangian linear relations (this semigroup includes
the Olshanski semigroup). We obtain the explicit realization of the Weil
representation of this semigroup in the Cartier model, i.e., in the space of
smooth sections of a certain line bundle on the $2n$-dimensional torus
$T^{2n}$. We show that operators of the representation are integral operators
whose kernels are theta-functions on $T^{4n}$.

35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat