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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| Định dạng: | Journal article |
| Ngôn ngữ: | English |
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Elsevier
2023
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| Truy cập trực tuyến: | https://scholar.dlu.edu.vn/handle/123456789/2322 https://doi.org/10.1016/j.jalgebra.2020.07.025 |
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oai:scholar.dlu.edu.vn:123456789-23222023-06-14T06:59:45Z An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians Đặng, Tuấn Hiệp Nguyen Chanh Tu 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. 565 564-581 2023-05-19T06:23:52Z 2023-05-19T06:23:52Z 2021-01 Journal article Bài báo đăng trên tạp chí thuộc ISI, bao gồm book chapter https://scholar.dlu.edu.vn/handle/123456789/2322 https://doi.org/10.1016/j.jalgebra.2020.07.025 en Journal of Algebra 0021-8693 Elsevier |
| institution |
Thư viện Trường Đại học Đà Lạt |
| collection |
Thư viện số |
| language |
English |
| description |
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. |
| format |
Journal article |
| author |
Đặng, Tuấn Hiệp Nguyen Chanh Tu |
| spellingShingle |
Đặng, Tuấn Hiệp Nguyen Chanh Tu An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians |
| author_facet |
Đặng, Tuấn Hiệp Nguyen Chanh Tu |
| author_sort |
Đặng, Tuấn Hiệp |
| title |
An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians |
| title_short |
An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians |
| title_full |
An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians |
| title_fullStr |
An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians |
| title_full_unstemmed |
An identity involving symmetric polynomials and the geometry of Lagrangian Grassmannians |
| title_sort |
identity involving symmetric polynomials and the geometry of lagrangian grassmannians |
| publisher |
Elsevier |
| publishDate |
2023 |
| url |
https://scholar.dlu.edu.vn/handle/123456789/2322 https://doi.org/10.1016/j.jalgebra.2020.07.025 |
| _version_ |
1778233849726107648 |