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. / Ph. D.
Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/77027 |
Date | 04 April 2017 |
Creators | Shifler, Ryan M. |
Contributors | Mathematics, Mihalcea, Constantin Leonardo, Haskell, Peter E., Orr, Daniel D., Shimozono, Mark M. |
Publisher | Virginia Tech |
Source Sets | Virginia Tech Theses and Dissertation |
Detected Language | English |
Type | Dissertation |
Format | ETD, application/pdf |
Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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