Minimum Quantum Degrees for Isotropic Grassmannians in Types B and C

Abstract

We give a formula in terms of Young diagrams to calculate the minimum positive integer d such that $$q^d$$ appears in the quantum product of two Schubert classes for the submaximal isotropic Grassmannians in types B and C. We do this by studying curve neighborhoods. We compute curve neighborhoods in several combinatorial models including k-strict partitions and a set of partitions where their inclusion is compatible with the Bruhat order.