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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| Những tác giả chính: | , |
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| Định dạng: | Research report |
| Ngôn ngữ: | English |
| Được phát hành: |
Journal of Algebra
2021
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| Những chủ đề: | |
| Truy cập trực tuyến: | http://scholar.dlu.edu.vn/handle/123456789/590 |
| Các nhãn: |
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| Thư viện lưu trữ: | Thư viện Trường Đại học Đà Lạt |
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| Tóm tắt: | 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. |
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