An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians

We first prove an identity involving symmetric polynomials. This identity leads us into exploring the geometry of Lagrangian Grassmannians. As an insight applications, we obtain a formula for the integral over the Lagrangian Grassmannian of a characteristic class of the tautological sub-bundle. More...

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Bibliographic Details
Published inJournal of algebra Vol. 565; pp. 564 - 581
Main Authors Hiep, Dang Tuan, Tu, Nguyen Chanh
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2021
Subjects
Equivariant cohomology
Gromov-Witten invariant
Interpolation
Lagrangian Grassmannian
Quantum cohomology
Schubert structure constant
Symmetric polynomial
secondary
Lagrangian Grassmannian
Interpolation
Gromov-Witten invariant
Equivariant cohomology
Symmetric polynomial
Quantum cohomology
primary
Schubert structure constant
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Summary:We first prove an identity involving symmetric polynomials. This identity leads us into exploring the geometry of Lagrangian Grassmannians. As an insight applications, we obtain a formula for the integral over the Lagrangian Grassmannian of a characteristic class of the tautological sub-bundle. Moreover, a relation to that over the ordinary Grassmannian and its application to the degree formula for the Lagrangian Grassmannian are given. Finally, we present further applications to the computation of Schubert structure constants and three-point, degree 1, genus 0 Gromov–Witten invariants of the Lagrangian Grassmannian. Some examples together with explicit computations are presented.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2020.07.025