Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: CFT approach to constraint operators for ($\beta$-deformed) hermitian
  one-matrix models   Since the ($\beta$-deformed) hermitian one-matrix models can be represented
as the integrated conformal field theory (CFT) expectation values, we construct
the operators in terms of the generators of the Heisenberg algebra such that
the constraints can be derived by inserting the constructed operators into the
integrated expectation values. In terms of the derived constraint operators and
one of the Virasoro constraint operators, we may construct the $W_{1+\infty}$
constraints with higher algebraic structures for these two matrix models. We
also give the total derivative operators associating with the derived
constraint operators and analyze their remarkable properties. Furthermore, we
explore the intrinsic connection between these constraint operators and
$W$-representations of some matrix models. For the Gaussian hermitian
one-matrix model in the external field and $\beta$-deformed $N\times N$ complex
matrix model, we investigate the superintegrability and derive the
corresponding character expansions from their $W$-representations. Moreover a
conjectured formula for the averages of Jack polynomials in the literature is
proved.

21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an