Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.14956 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915259313291264 |
|---|---|
| author | Bossinger, Lara Li, Jian-Rong |
| author_facet | Bossinger, Lara Li, Jian-Rong |
| contents | We study the homogeneous coordinate rings of partial flag varieties and Grassmannians in their Plücker embeddings and exhibit an embedding of the former into the latter. Both rings are cluster algebras and the embedding respects the cluster algebra structures in the sense that there exists a seed for the Grassmannian that restricts to a seed for the partial flag variety (\textit{i.e.} it is obtained by freezing and deleting some cluster variables).
The motivation for this project stems from the application of cluster algebras in scattering amplitudes: spinor helicity and momentum twistor varieties describe massless scattering without assuming dual conformal symmetry. Both may be obtained from Grassmanninas which model the dual conformal case. They are instances of partial flag varieties and their cluster structures reveal information for the scattering amplitudes. As an application of our main result we exhibit the relation between these cluster algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_14956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cluster structures on spinor helicity and momentum twistor varieties Bossinger, Lara Li, Jian-Rong Algebraic Geometry High Energy Physics - Theory Combinatorics Representation Theory 14M15, 13F60, 70S15 We study the homogeneous coordinate rings of partial flag varieties and Grassmannians in their Plücker embeddings and exhibit an embedding of the former into the latter. Both rings are cluster algebras and the embedding respects the cluster algebra structures in the sense that there exists a seed for the Grassmannian that restricts to a seed for the partial flag variety (\textit{i.e.} it is obtained by freezing and deleting some cluster variables). The motivation for this project stems from the application of cluster algebras in scattering amplitudes: spinor helicity and momentum twistor varieties describe massless scattering without assuming dual conformal symmetry. Both may be obtained from Grassmanninas which model the dual conformal case. They are instances of partial flag varieties and their cluster structures reveal information for the scattering amplitudes. As an application of our main result we exhibit the relation between these cluster algebras. |
| title | Cluster structures on spinor helicity and momentum twistor varieties |
| topic | Algebraic Geometry High Energy Physics - Theory Combinatorics Representation Theory 14M15, 13F60, 70S15 |
| url | https://arxiv.org/abs/2408.14956 |