Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A connection between the Kontsevich-Witten and Brezin-Gross-Witten
  tau-functions   The Brezin-Gross-Witten (BGW) model is one of the basic examples in the class
of non-eigenvalue unitary matrix models. The generalized BGW tau-function
$\tau_N$ was constructed from a one parametric deformation of the original BGW
model using the generalized Kontsevich model representation. It is a
tau-function of the KdV hierarchy for any value of $N\in\mathbb C$, where the
case $N=0$ reduces to the original BGW tau-function. In this paper, we present
a bosonic representation of $\tau_N$ in terms of the $W_{1+\infty}$ operators
that preserves the KP integrability. This allows us to establish a connection
between the (generalized) BGW and Kontsevich-Witten tau-functions using
$GL(\infty)$ operators, both considered as the basic building blocks in the
theory of matrix models and partition functions.

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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex