A proposed generalization of a full rim hook removal on partitions
April, 23 2022
MAA MD-DC-VA Section Meeting, Germantown, MD
In 2004 Fulton and Woodward gave a formula to calculate minimal quantum degrees that appear in the quantum product of two Schubert classes in general homogeneous space in G/P. They further specialize this result to the Type A Grassmannian in the language of partitions and rim hook removals. In this talk I will generalize Fulton and Woodward's specialization to all partial flags in Type A using Maya diagrams. Furthermore, I will show that the minimal quantum degree is unique with a combinatorial argument.
Curve neighborhoods of Schubert varieties of the odd symplectic Grassmannian
November, 18 2021
Groups, Algebra, and Geometry Seminar, Poitiers, France
Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian
February, 22 2017
Algebra Seminar, New Brunswick, NJ
The odd symplectic Grassmannian IG:=IG(k, 2n+1) parametrizes k dimensional subspaces of C2n+1 which are isotropic with respect to a general (necessarily degenerate) symplectic form. The odd symplectic group acts on IG with two orbits, and IG is itself a smooth Schubert variety in the submaximal isotropic Grassmannian IG(k, 2n+2). We use the technique of curve neighborhoods to prove a Chevalley formula in the equivariant quantum cohomology of IG, i.e. a formula to multiply a Schubert class by the Schubert divisor class. This generalizes a formula of Pech in the case k=2, and it gives an algorithm to calculate any quantum multiplication in the equivariant quantum cohomology ring. The current work is joint with L. Mihalcea.
