On two notions of total positivity for generalized partial flag varieties of classical Lie types
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916457222242304 |
|---|---|
| author | Barkley, Grant Boretsky, Jonathan Eur, Christopher Gao, Jiyang |
| author_facet | Barkley, Grant Boretsky, Jonathan Eur, Christopher Gao, Jiyang |
| contents | For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory, tropical geometry, and the theory of total positivity. Bloch and Karp furthermore characterized the (type A) partial flag varieties for which the two notions of positivity similarly coincide. We characterize the symplectic (type C) and odd-orthogonal (type B) partial flag varieties for which Lusztig's total positivity coincides with Plucker positivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On two notions of total positivity for generalized partial flag varieties of classical Lie types Barkley, Grant Boretsky, Jonathan Eur, Christopher Gao, Jiyang Combinatorics Algebraic Geometry Representation Theory For Grassmannians, Lusztig's notion of total positivity coincides with positivity of the Plucker coordinates. This coincidence underpins the rich interaction between matroid theory, tropical geometry, and the theory of total positivity. Bloch and Karp furthermore characterized the (type A) partial flag varieties for which the two notions of positivity similarly coincide. We characterize the symplectic (type C) and odd-orthogonal (type B) partial flag varieties for which Lusztig's total positivity coincides with Plucker positivity. |
| title | On two notions of total positivity for generalized partial flag varieties of classical Lie types |
| topic | Combinatorics Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2410.11804 |