论文标题
通用$ \ text {gl} _n \ rtimes \！<\！σ\！\！\！$ - character品种：未分支的情况
E-Polynomials of Generic $\text{GL}_n\rtimes\!<\!σ\!>\!~$-Character Varieties: Unbranched Case
论文作者
论文摘要
对于任何无分支的双重覆盖紧凑的Riemann表面，我们研究了在全球意义上统一的相关角色，我们称之为$ \ text {gl} _n \ rtimes \！我们在表面上介绍$ K> 0 $穿刺，并将穿刺周围的单一个限制在$ \ text {gl} _n $中，并使用$ \ text {gl} _n（q）$ \ text {gl} _n $中的通用半简单的共轭类课程。结果表示为某些对称函数的内部产物。然后，我们被带到了混合霍奇多项式的猜想公式，该公式是由（修改的）麦克唐纳（MacDonald）多项式制造的，它们的自我配对和花圈麦克唐纳（MacDonald）多项式的自我配对。
For any unbranched double covering of compact Riemann surfaces, we study the associated character varieties that are unitary in the global sense, which we call $\text{GL}_n\rtimes\!<\!σ\!>\!~$-character varieties. We introduce $k>0$ punctures on the surface, and restrict the monodromies around the punctures to generic semi-simple conjugacy classes in $\text{GL}_n$, and compute the E-polynomials of these character varieties using the character table of $\text{GL}_n(q)$. 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.
