论文标题
交叉路口综合体和未受到的$ l $ factors
Intersection complexes and unramified $L$-factors
论文作者
论文摘要
令X为仿射球形品种，可能是单数，并且是其弧形空间的$ l^+x $。 $ l^+x $的交叉路口复合物，或者更确切地说，其有限维正式模型与局部未受到的L功能的特殊值有关。此类关系以前是在Braverman-Finkelberg-Gaitsgory-Mirkovic中建立的，用于通过抛物线寄生虫的一能自由基和Bouthier-ngo-sakellaridis仿效还原群体的商封闭，以染成圆磨和L-肌体。在本文中，我们计算了大量球形G型的相交复合体，其双重组等于Langlands双重组的G，以及附近其附近的缠扰性X的茎上X的horossical cycles cycles x的horossical cycles x的horossical cycles。我们以kashiwara crystal senitient to to to to to to the Inimient contination the dimimentim dimimentim in the dimimentim the dimemention的答案来表达的答案。 X的估值。在许多情况下，我们证明了后者的猜想。在捆绑功能词典下，我们的计算给出了$ l^+x $的plancherel密度的公式，这是一大型球形品种的局部L值的比率。
Let X be an affine spherical variety, possibly singular, and $L^+X$ its arc space. The intersection complex of $L^+X$, or rather of its finite-dimensional formal models, is conjectured to be related to special values of local unramified L-functions. Such relationships were previously established in Braverman-Finkelberg-Gaitsgory-Mirkovic for the affine closure of the quotient of a reductive group by the unipotent radical of a parabolic, and in Bouthier-Ngo-Sakellaridis for toric varieties and L-monoids. In this paper, we compute this intersection complex for the large class of those spherical G-varieties whose dual group is equal to the Langlands dual group of G, and the stalks of its nearby cycles on the horospherical degeneration of X. We formulate the answer in terms of a Kashiwara crystal, which conjecturally corresponds to a finite-dimensional representation of the dual group determined by the set of B-invariant valuations on X. 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 of $L^+X$ as a ratio of local L-values for a large class of spherical varieties.
