Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twisted Representations of Algebra of $q$-Difference Operators, Twisted
  $q$-$W$ Algebras and Conformal Blocks   We study certain representations of quantum toroidal $\mathfrak{gl}_1$
algebra for $q=t$. We construct explicit bosonization of the Fock modules
$\mathcal{F}_u^{(n',n)}$ with a nontrivial slope $n'/n$. As a vector space, it
is naturally identified with the basic level 1 representation of affine
$\mathfrak{gl}_n$. We also study twisted $W$-algebras of $\mathfrak{sl}_n$
acting on these Fock modules. As an application, we prove the relation on
$q$-deformed conformal blocks which was conjectured in the study of
$q$-deformation of isomonodromy/CFT correspondence.

12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics