# An analogue of the Grothendieck-Springer resolution for symmetric spaces

## TL;DR

This paper generalizes Grothendieck's resolution to symmetric spaces, enabling new insights into automorphism sheaves and Springer theory applications within this context.

## Contribution

It introduces a novel resolution for symmetric pairs, extending classical geometric tools to new settings in representation theory.

## Key findings

- Constructed a resolution for symmetric pairs
- Proved a relative automorphism sheaf result
- Provided partial progress in Springer theory for symmetric spaces

## Abstract

Motivated by questions in 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.