Motivated by questions from the study of relative trace formulae, we construct a generalization of Grothendieck’s simultaneous resolution over the regular locus of certain symmetric pairs. We use this space to prove a relative version of results of Donagi and Gaitsgory about the automorphism sheaf of regular stabilizers. We also obtain partial results toward applications in Springer theory for symmetric spaces.

中文翻译：

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对称空间的Grothendieck–Springer分辨率的类似物

出于研究相对迹线公式的问题的考虑，我们构造了一定对称对的正则轨迹上格罗腾迪克同时分解的推广。我们使用该空间来证明Donagi和Gaitsgory关于常规稳定剂的同构捆的结果的相对版本。对于对称空间在Springer理论中的应用，我们也获得了部分结果。