Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19313 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916709547376640 |
|---|---|
| author | Brito, Matheus Chari, Vyjayanthi |
| author_facet | Brito, Matheus Chari, Vyjayanthi |
| contents | We determine the set of dominant $\ell$--weights in the Weyl (or standard) modules for quantum affine $A_n$. We then prove that the space of homomorphisms between standard modules is at most one-dimensional and give a necessary and sufficient condition for equality to hold. We also describe the socle of the standard module and prove that the socle is simple for large $n$. Finally, we give applications of our results to mixed Weyl modules, calculating extensions in the category and identify new families of tensor subcategories of finite dimensional representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19313 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On dominant $\ell$--weights and maps between Weyl modules for quantum affine $A_n$ Brito, Matheus Chari, Vyjayanthi Quantum Algebra Representation Theory We determine the set of dominant $\ell$--weights in the Weyl (or standard) modules for quantum affine $A_n$. We then prove that the space of homomorphisms between standard modules is at most one-dimensional and give a necessary and sufficient condition for equality to hold. We also describe the socle of the standard module and prove that the socle is simple for large $n$. Finally, we give applications of our results to mixed Weyl modules, calculating extensions in the category and identify new families of tensor subcategories of finite dimensional representations. |
| title | On dominant $\ell$--weights and maps between Weyl modules for quantum affine $A_n$ |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2504.19313 |