Quantum loop groups for symmetric Cartan matrices
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917195192205312 |
|---|---|
| author | Neguţ, Andrei |
| author_facet | Neguţ, Andrei |
| contents | We introduce a quantum loop group associated to a general symmetric Cartan matrix, by imposing just enough relations between the usual generators $\{e_{i,k}, f_{i,k}\}_{i \in I, k \in \mathbb{Z}}$ in order for the natural Hopf pairing between the positive and negative halves of the quantum loop group to be perfect. As an application, we describe the localized K-theoretic Hall algebra of any quiver without loops, endowed with a particularly important $\mathbb{C}^*$ action. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05504 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantum loop groups for symmetric Cartan matrices Neguţ, Andrei Representation Theory Quantum Algebra We introduce a quantum loop group associated to a general symmetric Cartan matrix, by imposing just enough relations between the usual generators $\{e_{i,k}, f_{i,k}\}_{i \in I, k \in \mathbb{Z}}$ in order for the natural Hopf pairing between the positive and negative halves of the quantum loop group to be perfect. As an application, we describe the localized K-theoretic Hall algebra of any quiver without loops, endowed with a particularly important $\mathbb{C}^*$ action. |
| title | Quantum loop groups for symmetric Cartan matrices |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2207.05504 |