Toward a type B(n) geometric Littlewood-Richardson Rule
Date
2007
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Abstract
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).
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Subject
algebraic geometry
checker games
degenerations
Grassmannian
Littlewood-Richardson Rule
Schubert calculus
vector spaces
mathematics