Toward a type B(n) geometric Littlewood-Richardson Rule - Davis, Diane E., author; Kley, Holger, advisor (Colorado State University. Libraries, 2007)
We conjecture a geometric Littlewood-Richardson Rule for the maximal orthogonal Grassmannian and make significant advances in the proof of this conjecture. We consider Schubert calculus in the presence of a nondegenerate symmetric bilinear form on an odd-dimensional vector space (the type Bn setting) and use degenerations to understand intersections of Schubert varieties in the odd orthogonal Grassmannian. We describe the degenerations using combinatorial objects called checker games. This work is closely related to Vakil's Geometric Littlewood-Richardson Rule (Annals of Mathematics, 164).
Keywords: algebraic geometry; checker games; degenerations; Grassmannian; Littlewood-Richardson Rule; Schubert calculus; vector spaces; mathematics