Quadratic degenerations of odd-orthogonal Schubert varieties

This paper is the second in a series leading to a type B_n geometric Littlewood-Richardson rule. The rule will give an interpretation of the B_n Littlewood-Richardson numbers as an intersection of two odd-orthogonal Schubert varieties and will consider a sequence of linear and quadratic deformations of the intersection into a union of odd-orthogonal Schubert varieties. This paper describes the setup for the rule and specifically addresses results for quadratic deformations, including a proof that at each quadratic degeneration, the results occur with multiplicity one. This work is strongly influenced by Vakil’s 14].