The elliptic Hall algebra and the double Dyck path algebra
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915166930599936 |
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| author | Gonzalez, Nicolle Gorsky, Eugene Simental, Jose |
| author_facet | Gonzalez, Nicolle Gorsky, Eugene Simental, Jose |
| contents | We show that the positive half $\mathcal{E}_{q,t}^{>}$ of the elliptic Hall algebra is embedded as a natural spherical subalgebra inside the double Dyck path algebra $\mathbb{B}_{q,t}$ introduced by Carlsson, Mellit and the second author. For this, we use the Ding-Iohara-Miki presentation of the elliptic Hall algebra and identify the generators inside $\mathbb{B}_{q,t}$. In order to obtain the entire elliptic Hall algebra $\mathcal{E}_{q,t}$, we define a ``double'' $\mathbb{DB}_{q,t}$ of the double Dyck path algebra, together with its positive and negative subalgebras and an involution that exchanges them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16113 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The elliptic Hall algebra and the double Dyck path algebra Gonzalez, Nicolle Gorsky, Eugene Simental, Jose Representation Theory Quantum Algebra We show that the positive half $\mathcal{E}_{q,t}^{>}$ of the elliptic Hall algebra is embedded as a natural spherical subalgebra inside the double Dyck path algebra $\mathbb{B}_{q,t}$ introduced by Carlsson, Mellit and the second author. For this, we use the Ding-Iohara-Miki presentation of the elliptic Hall algebra and identify the generators inside $\mathbb{B}_{q,t}$. In order to obtain the entire elliptic Hall algebra $\mathcal{E}_{q,t}$, we define a ``double'' $\mathbb{DB}_{q,t}$ of the double Dyck path algebra, together with its positive and negative subalgebras and an involution that exchanges them. |
| title | The elliptic Hall algebra and the double Dyck path algebra |
| topic | Representation Theory Quantum Algebra |
| url | https://arxiv.org/abs/2502.16113 |