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We express a Schubert expansion of the Chern-Mather class for Schubertvarieties in the even orthogonal Grassmannian via integrals involving Pfaffiansand pushforward of the small resolutions in the sense of IntersectionCohomology (IH) constructed by Sankaran and Vanchinathan, instead of the Nashblowup. The equivariant localization is employed to show the way of computingthe integral. As a byproduct, we present the computations. For analogy and thecompletion of the method in ordinary Grassmannians, we also suggestKazhdan-Lusztig classes associated to Schubert varieties in the Lagrangian andodd orthogonal Grassmannian.

Mather classes of Schubert varieties via small resolutions