Equivariant $K$-theory of even-dimensional complex quadrics

Abstract

The aim of this paper is to describe the torus equivariant $K$-ring of even-dimensional complex quadrics by studying the graph equivariant $K$-theory of their corresponding GKM graphs. This involves providing a presentation for its graph equivariant $K$- ring in terms of generators and relations. This parallels the description of the equivariant cohomology ring of even-dimensional complex quadrics due to Kuroki.