An analogue of the Grothendieck–Springer resolution for symmetric spaces

Leslie, Spencer

doi:10.2140/ant.2021.15.69

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An analogue of the Grothendieck–Springer resolution for symmetric spaces

Spencer Leslie

Vol. 15 (2021), No. 1, 69–107

DOI: 10.2140/ant.2021.15.69

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

Vol. 15, No. 1, 2021