论文标题
降低惠特克系数的不断变化的还原组
Non-vanishing of geometric Whittaker coefficients for reductive groups
论文作者
论文摘要
我们证明，尖锐的自动型D模块具有非散热器系数，从GL_N到一般还原组的几何Langlands计划中概括了已知结果。关键工具是对Whittaker系数的微局部解释。我们在几何兰兰兹环境中建立了各种精确性，可能具有独立感兴趣。具体而言，我们表明Hecke函子在钢化D模块的类别上是T型的，从而增强了GL_N步态的经典结果（具有不同的假设）。我们还表明，Whittaker系数函数是具有nilpotent奇异支撑的滑轮的T型外观。我们结果的另一个结果是，受纠正的，受限制的几何兰兰斯的猜想必须是t-精神。我们应用结果表明，对于适当不可还原的局部系统，惠特克·纳尔赛（Whittaker-Norz）的hecke eigensheaves是bun_g的每个连接组件上不可还原的不可修复的绳索。
We prove that cuspidal automorphic D-modules have non-vanishing Whittaker coefficients, generalizing known results in the geometric Langlands program from GL_n to general reductive groups. The key tool is a microlocal interpretation of Whittaker coefficients. We establish various exactness properties in the geometric Langlands context that may be of independent interest. Specifically, we show Hecke functors are t-exact on the category of tempered D-modules, strengthening a classical result of Gaitsgory (with different hypotheses) for GL_n. We also show that Whittaker coefficient functors are t-exact for sheaves with nilpotent singular support. An additional consequence of our results is that the tempered, restricted geometric Langlands conjecture must be t-exact. We apply our results to show that for suitably irreducible local systems, Whittaker-normailzed Hecke eigensheaves are perverse sheaves that are irreducible on each connected component of Bun_G.
