K-classes of delta-matroids and equivariant localization

Abstract

Delta-matroids are “type B” generalizations of matroids in the same way that maximal orthogonal Grassmannians are generalizations of Grassmannians. A delta-matroid analogue of the Tutte polynomial of a matroid is the interlace polynomial. We give a geometric interpretation for the interlace polynomial via the K K -theory of maximal orthogonal Grassmannians. To do so, we develop a new Hirzebruch–Riemann–Roch-type formula for the type B permutohedral variety.