Intersection complexes and unramified ?-factors
Intersection complexes and unramified ?-factors
复制标题
交叉复合体和未分支的 ?-因子
DOI：
10.1090/jams/990
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发表时间：
2022
影响因子：
3.9
通讯作者：
Wang, Jonathan
中科院分区：
文献类型：
--
作者：
Sakellaridis, Yiannis;Wang, Jonathan
设是一个仿射球面簇，可能是奇异的，它的弧空间。的交集复杂的，或者更确切地说，它的有限维形式模型，被证明是有关的特殊值的局部unramified-functions。这种关系以前在布雷弗曼-芬克尔伯格-盖茨戈里-米尔科维奇（Braverman-Finkelberg-Gaitsgory-Mirković）中建立，用于抛物的幂幺根式的约化群的商的仿射闭包，在Bouthier-Ngô-Sakellarovich中建立，用于复曲面簇和-幺半群。在本文中，我们计算了对偶群等于的一类球簇的交复形及其邻近圈的茎在的次球退化上的交复形。我们制定的答案在柏原晶体，这在几何上对应于一个有限维表示所确定的一组不变的估值。我们证明了后者猜想在许多情况下。在层函数字典下，我们的计算给出了IC函数的Plancherel密度公式，作为一大类球面簇的局部值之比。引用
Letbe an affine spherical variety, possibly singular, andits arc space. The intersection complex of, or rather of its finite-dimensional formal models, is conjectured to be related to special values of local unramified-functions. Such relationships were previously established in Braverman–Finkelberg–Gaitsgory–Mirković for the affine closure of the quotient of a reductive group by the unipotent radical of a parabolic, and in Bouthier–Ngô–Sakellaridis for toric varieties and-monoids. In this paper, we compute this intersection complex for the large class of those spherical-varieties whose dual group is equal to, and the stalks of its nearby cycles on the horospherical degeneration of. We formulate the answer in terms of a Kashiwara crystal, which conjecturally corresponds to a finite-dimensional-representation determined by the set of-invariant valuations on. We prove the latter conjecture in many cases. Under the sheaf–function dictionary, our calculations give a formula for the Plancherel density of the IC function ofas a ratio of local-values for a large class of spherical varieties. References