Conjecture O holds for the odd symplectic Grassmannian
Abstract
Property O, introduced by Galkin et al. for arbitrary complex, Fano manifolds X, is a statement about the eigenvalues of the linear operator obtained by the quantum multiplication by the anticanonical class of X. We prove that property O holds in the case when X = IG(k, 2n + 1) is an odd symplectic Grassmannian. The proof uses the combinatorics of the recently found quantum Chevalley formula for IG(k, 2n + 1), together with the Perron–Frobenius theory of nonnegative matrices.
Faculty Members
- Changzheng Li - School of MathematicsSun Yat‐sen UniversityGuangzhou 510275 P. R. China
- Leonardo C. Mihalcea - Department of MathematicsVirginia Tech University460 McBryde Hall Blacksburg VA 24060 USA
- Ryan M. Shifler - Department of Mathematics and Computer ScienceSalisbury UniversityHenson Science Hall Salisbury MD 21801 USA
Themes
- symplectic Grassmannians
- eigenvalues
- Property O
- mathematical structures
- quantum multiplication
- Fano manifolds
Categories
- Mathematics, general
- Physical sciences
- Algebra and number theory
- Physics
- Mathematics
- Mathematics and statistics
- Physics and physical sciences nec
- Materials sciences
- Applied mathematics, general
- Computational and applied mathematics
- Materials chemistry and materials science nec
- Theoretical and mathematical physics
- Applied mathematics