论文标题
对与$ w相关的shi品种不可约组件的对称组动作（\ widetilde {a} _n）$
A symmetric group action on the irreducible components of the Shi variety associated to $W(\widetilde{A}_n)$
论文作者
论文摘要
令$ w_a $为具有相应有限根系$φ$的仿射Weyl组。在\ cite {jys1} jian-yi shi中，$φ^+$ - 整数$（k（w，α））_ {α\ inφ^+} $表征了每个元素$ w \ in w_a $ in w_a $。在\ cite {nc1}中给出了系数$ k（w，α）$的新解释。此描述使我们定义了一个仿射品种$ \ wideHat {x} _ {w_a} $，称为$ w_a $的shi品种，其积分积分与$ w_a $进行了两次射击。事实证明，这种品种具有多个不可约组件，这些组件的集合表示为$ h^0（\ widehat {x} _ {w_a}）$，承认了许多有趣的属性。尤其是$ w_a $对其进行。在本文中，我们表明，$ \ wideHat {x} _ {w（\ widetilde {a} _n）} $的一组不可减至的组件与$（1〜2〜 \ cdots〜n+1）\ in W（a_n）= s_ n+1} $的共轭类别均与$（1〜2〜 \ cdots〜n+n+1）\。我们还计算了$ h^0（\ wideHat {x} _ {w（\ widetilde {a} _n）}）$ h^0（\ wideHat {x} _n）}）$ $ w（a_n）$的动作。
Let $W_a$ be an affine Weyl group with corresponding finite root system $Φ$. In \cite{JYS1} Jian-Yi Shi characterized each element $w \in W_a$ by a $ Φ^+$-tuple of integers $(k(w,α))_{α\in Φ^+}$ subject to certain conditions. In \cite{NC1} a new interpretation of the coefficients $k(w,α)$ is given. This description led us to define an affine variety $\widehat{X}_{W_a}$, called the Shi variety of $W_a$, whose integral points are in bijection with $W_a$. It turns out that this variety has more than one irreducible component, and the set of these components, denoted $H^0(\widehat{X}_{W_a})$, admits many interesting properties. In particular the group $W_a$ acts on it. In this article we show that the set of irreducible components of $\widehat{X}_{W(\widetilde{A}_n)}$ is in bijection with the conjugacy class of $(1~2~\cdots~n+1) \in W(A_n) = S_{n+1}$. We also compute the action of $W(A_n)$ on $H^0(\widehat{X}_{W(\widetilde{A}_n)})$.
