  In this paper we establish Springer correspondence for the symmetric pair
$(\mathrm{SL}(N),\mathrm{SO}(N))$ using Fourier transform, parabolic induction
functor, and a nearby cycle sheaves construction due to Grinberg. As
applications, we obtain results on cohomology of Hessenberg varieties and
geometric constructions of irreducible representations of Hecke algebras of
symmetric groups at $q=-1$.
