K Amini: A Bridge Between the Quantum K-Theory of the Grassmannian and that of Its cotangent bundle скачать в хорошем качестве

K Amini: A Bridge Between the Quantum K-Theory of the Grassmannian and that of Its cotangent bundle

Abstract: The relationship between the quantum K-ring of a variety and that of its cotangent bundle lies at the intersection of algebraic geometry, representation theory, and integrable systems. Givental's J-function and the quasimap vertex function are two fundamental enumerative objects that govern the quantum K-theory of smooth varieties and Nakajima quiver varieties, respectively. We introduce a K-theoretic operator, called balancing, which provides an algebraic mechanism to lift the J-function of the Grassmannian to the vertex function of its cotangent bundle, thereby revealing an explicit geometric interpretation. We further show that the Bethe-Ansatz equations for cotangent bundle of projective spaces, which are expected to encode the relations in its quantum K-ring, arise as lifts of the quantum K-theoretic relations of the projective spaces via the balancing operators.