Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: E-Polynomials of Generic $\text{GL}_n\rtimes\!<\!\sigma\!>\!~$-Character
  Varieties: Branched Case   For any branched double covering of compact Riemann surfaces, we consider the
associated character varieties that are unitary in the global sense, which we
call $\text{GL}_n\rtimes\!<\!\sigma\!>\!~$-character varieties. We restrict the
monodromies around the ramification points to generic semi-simple conjugacy
classes contained in $\text{GL}_n\sigma$, and compute the E-polynomials of
these character varieties using the character table of
$\text{GL}_n(q)\rtimes\!<\!\sigma\!>\!$. The result is expressed as the inner
product of certain symmetric functions associated to the wreath products
$(\mathbb{Z}/2\mathbb{Z})^N\rtimes\mathfrak{S}_N$. We are then led to a
conjectural formula for the mixed Hodge polynomial, which involves (modified)
Macdonald polynomials and wreath Macdonald polynomials.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con