E-polynomials of generic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mo form="prefix">GL</mml:mo> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>⋊</mml:mo> <mml:mrow> <mml:mo>〈</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>〉</m

For any unbranched double covering of a compact Riemann surface, we study the associated character varieties that are unitary in the global sense, which we call <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mo form="prefix">GL</mml:mo> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>⋊</mml:mo> <mml:mrow> <mml:mo>〈</mml:mo> <mml:mi>σ</mml:mi> <mml:mo>〉</mml:mo> </mml:mrow> </mml:mrow> </mml:math> -character varieties. We introduce <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> punctures on the surface, restrict the monodromies around the punctures to generic semi-simple conjugacy classes in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mo form="prefix">GL</mml:mo> <mml:mi>n</mml:mi> </mml:msub> </mml:math> , and compute the E-polynomials of these character varieties using the character table of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mo form="prefix">GL</mml:mo> <mml:mi>n</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>q</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . The result is expressed as the inner product of certain symmetric functions. We are then led to a conjectural formula for the mixed Hodge polynomial, which is built out of (modified) Macdonald polynomials, their self-pairings, and self-pairings of wreath Macdonald polynomials.