Vol. 15, No. 1, 2021

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An analogue of the Grothendieck–Springer resolution for symmetric spaces

Spencer Leslie

Vol. 15 (2021), No. 1, 69–107
Abstract

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.

Keywords
symmetric pair, regular stabilizers, resolution of singularities, Springer theory, relative trace formulae
Mathematical Subject Classification 2010
Primary: 20G05
Secondary: 17B08, 32S45
Milestones
Received: 19 April 2019
Revised: 30 April 2020
Accepted: 29 July 2020
Published: 1 March 2021
Authors
Spencer Leslie
Duke University
Durham, NC
United States