A uniform trigonometric R-matrix for the exceptional series
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_ | 1866915144990195712 |
|---|---|
| author | Westbury, Bruce W. Zinn-Justin, Paul |
| author_facet | Westbury, Bruce W. Zinn-Justin, Paul |
| contents | The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras includes the five exceptional Lie algebras. We give a uniform trigonometric $R$-matrix for the exceptional series in the representation $L\oplus I$, where $L$ is the quantum deformation of the adjoint representation and $I$ is the trivial representation. We construct a sixteen dimensional algebra, $A^\square(\mathit2)$, which interpolates the algebras $\mathrm{End}(\otimes^2(L\oplus I))$ and a 287 dimensional algebra, $A^\square(\mathit3)$, which interpolates the algebras $\mathrm{End}(\otimes^3(L\oplus I))$. The $R$-matrix lives in $A^\square(\mathit2)$ and satisfies the Yang-Baxter equation in $A^\square(\mathit3)$; it interpolates the trigonometric $R$-matrices for the points in the exceptional series. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_01348 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A uniform trigonometric R-matrix for the exceptional series Westbury, Bruce W. Zinn-Justin, Paul Representation Theory Mathematical Physics Quantum Algebra The exceptional series is a finite list of points on a projective line with a simple Lie algebra attached to each point. This list of Lie algebras includes the five exceptional Lie algebras. We give a uniform trigonometric $R$-matrix for the exceptional series in the representation $L\oplus I$, where $L$ is the quantum deformation of the adjoint representation and $I$ is the trivial representation. We construct a sixteen dimensional algebra, $A^\square(\mathit2)$, which interpolates the algebras $\mathrm{End}(\otimes^2(L\oplus I))$ and a 287 dimensional algebra, $A^\square(\mathit3)$, which interpolates the algebras $\mathrm{End}(\otimes^3(L\oplus I))$. The $R$-matrix lives in $A^\square(\mathit2)$ and satisfies the Yang-Baxter equation in $A^\square(\mathit3)$; it interpolates the trigonometric $R$-matrices for the points in the exceptional series. |
| title | A uniform trigonometric R-matrix for the exceptional series |
| topic | Representation Theory Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2406.01348 |