Pieri rules for the \(K\)-theory of cominuscule Grassmannians (Q2904012)

The \(K\)-theory ring of a homogeneous space \(X\) has a natural basis parameterized by the Schubert varieties of \(X\). An important question in enumerative geometry is the determination of the structure constants of the ring with respect to this basis. The paper under review studies the special case when \(X\) is a cominuscule Grassmannian, and one of the multiplied classes corresponds to a special Schubert variety (Pieri rule). The authors describe the structure constants both as integers determined by positive recursive identities and as the number of certain combinatorial objects called tableaux. The result reproves a formula of Lenard in type \(A\), and is new for orthogonal and Lagrangian Grassmannians. The proof is based on calculating sheaf Euler characteristics of special triple intersections of Schubert varieties.