论文标题
通用$ \ text {gl} _n \ rtimes \！<\！σ\！\！\！$ - character品种：分支案例的e-polynomials
E-Polynomials of Generic $\text{GL}_n\rtimes\!<\!σ\!>\!~$-Character Varieties: Branched Case
论文作者
论文摘要
对于紧凑的Riemann表面的任何分支双重覆盖，我们考虑了在全球意义上是统一的相关字符品种，我们称之为$ \ text {gl} _n \ rtimes \！<\！<\！σ\！\！\！\！\！我们限制了分支周围的单一个指向的单调指向$ \ text {gl}_nσ$中包含的通用半简单共轭类，并使用$ \ text {gl} _n（q）_n（q）\ rtimes \ rtimes \！<\ \ \！$！$！$！$！$！$！$ \！$！结果表示为与花圈产品相关的某些对称函数的内部产物$（\ mathbb {z}/2 \ mathbb {z}）^n \ rtimes \ mathfrak {s} _n $。然后，我们被带到混合霍奇多项式的猜想公式，该公式涉及（修改）麦克唐纳多项式和麦克唐纳多项式的花环。
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 $\text{GL}_n\rtimes\!<\!σ\!>\!~$-character varieties. We restrict the monodromies around the ramification points to generic semi-simple conjugacy classes contained in $\text{GL}_nσ$, and compute the E-polynomials of these character varieties using the character table of $\text{GL}_n(q)\rtimes\!<\!σ\!>\!$. 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.
