I tiakina i:
| Kaituhi matua: | |
|---|---|
| Hōputu: | Preprint |
| I whakaputaina: |
2025
|
| Ngā marau: | |
| Urunga tuihono: | https://arxiv.org/abs/2502.08039 |
| Ngā Tūtohu: |
Tāpirihia he Tūtohu
Kāore He Tūtohu, Me noho koe te mea tuatahi ki te tūtohu i tēnei pūkete!
|
Rārangi ihirangi:
- We produce 2-representations of the positive part of affine quantum enveloping algebras on their finite-dimensional counterparts in type $A_n$. These 2-representations naturally extend the right-multiplication 2-representation of $U_q^+(\mathfrak{sl}_{n+1})$ on itself and are closely related to evaluation morphisms of quantum groups. We expect that our 2-representation exists in all simple types and show that the corresponding 1-representation exists in types $D_4$ and $C_2$. We also show that a certain quotient of our 1-representation in type $A_n$ is isomorphic to a prefundamental representation. We use this to provide a new proof of the prefundamental representation character formulas in these cases.