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.
"An analogue of the Grothendieck–Springer resolution for symmetric spaces." Algebra Number Theory 15 (1) 69 - 107, 2021. https://doi.org/10.2140/ant.2021.15.69