Equivariant Quantum Cohomology of the Odd Symplectic Grassmannian

The odd symplectic Grassmannian IG := IG(k, 2n + 1) parametrizes k dimensional subspaces of C^2n+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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2017

Author dc:creator

• Shifler, Ryan M.

Chair dc:contributor.committeechair

• Mihalcea, Constantin Leonardo

Committee members dc:contributor.committeemember

• Haskell, Peter E.
• Orr, Daniel D.
• Shimozono, Mark M.

• odd symplectic
• quantum cohomology
• Chevalley formula

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

vt_gsexam:9847

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/77027