Wreath Macdonald polynomials as eigenstates
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2019
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866911151541977088 |
|---|---|
| author | Wen, Joshua Jeishing |
| author_facet | Wen, Joshua Jeishing |
| contents | We show that the wreath Macdonald polynomials for $\mathbb{Z}/\ell\mathbb{Z}\wrΣ_n$, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra $U_{\mathfrak{q},\mathfrak{d}}(\ddot{\mathfrak{sl}}_\ell)$, diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods, and we also obtain a new proof of existence of wreath Macdonald polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1904_05015 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Wreath Macdonald polynomials as eigenstates Wen, Joshua Jeishing Quantum Algebra Combinatorics Representation Theory 81R50, 05E05 We show that the wreath Macdonald polynomials for $\mathbb{Z}/\ell\mathbb{Z}\wrΣ_n$, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra $U_{\mathfrak{q},\mathfrak{d}}(\ddot{\mathfrak{sl}}_\ell)$, diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods, and we also obtain a new proof of existence of wreath Macdonald polynomials. |
| title | Wreath Macdonald polynomials as eigenstates |
| topic | Quantum Algebra Combinatorics Representation Theory 81R50, 05E05 |
| url | https://arxiv.org/abs/1904.05015 |