On the $$E$$E-polynomials of a family of $${ ext {Sl}}_n$$Sln-character varieties
On the $$E$$E-polynomials of a family of $${ ext {Sl}}_n$$Sln-character varieties
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关于 $${ ext {Sl}}_n$$Sln 字符变体族的 $$E$$E 多项式
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发表时间：
2015
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通讯作者：
M. Mereb
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作者：
M. Mereb
We find the $$E$$E-polynomials of a family of twisted character varieties $${mathcal {M}}({ ext {Sl}}_n)$$M(Sln) of Riemann surfaces by proving they have polynomial count, and applying a result of Katz regarding the counting functions. To count the number of $$mathbb {F}_q$$Fq-points of these varieties as a function of $$q,$$q, we invoke a formula from Frobenius. Our calculations make use of the character tables of $${ ext {Sl}}_n(q),$$Sln(q), partially computed by Lehrer, and a result of Hanlon on the Möbius function of a fixed subposet of set-partitions. We compute the Euler characteristic of the $${mathcal {M}}({ ext {Sl}}_n)$$M(Sln) with these polynomials, and show they are connected.
We find the $$E$$E-polynomials of a family of twisted character varieties $${mathcal {M}}({ ext {Sl}}_n)$$M(Sln) of Riemann surfaces by proving they have polynomial count, and applying a result of Katz regarding the counting functions. To count the number of $$mathbb {F}_q$$Fq-points of these varieties as a function of $$q,$$q, we invoke a formula from Frobenius. Our calculations make use of the character tables of $${ ext {Sl}}_n(q),$$Sln(q), partially computed by Lehrer, and a result of Hanlon on the Möbius function of a fixed subposet of set-partitions. We compute the Euler characteristic of the $${mathcal {M}}({ ext {Sl}}_n)$$M(Sln) with these polynomials, and show they are connected.