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

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.

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