Rational Cherednik Algebras and Torus Knot Invariants
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866910348307595264 |
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| author | Ma, Xinchun |
| author_facet | Ma, Xinchun |
| contents | The HOMFLY polynomial of the $(m,n)$ torus knot $T_{m,n}$ can be extracted from the doubly graded character of the finite-dimensional representation $\mathrm{L}_{\frac{m}{n}}$ of the type $A_{n-1}$ rational Cherednik algebra as observed by Gorsky, Oblomkov, Rasmussen and Shende. It is furthermore conjectured that one can obtain the triply-graded Khovanov-Rozansky homology of $T_{m,n}$ by considering a certain filtration on $\mathrm{L}_{\frac{m}{n}}$. In this paper, we show that two of the proposed candidates, the algebraic filtration and the inductive filtration, are equal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18770 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rational Cherednik Algebras and Torus Knot Invariants Ma, Xinchun Representation Theory Combinatorics The HOMFLY polynomial of the $(m,n)$ torus knot $T_{m,n}$ can be extracted from the doubly graded character of the finite-dimensional representation $\mathrm{L}_{\frac{m}{n}}$ of the type $A_{n-1}$ rational Cherednik algebra as observed by Gorsky, Oblomkov, Rasmussen and Shende. It is furthermore conjectured that one can obtain the triply-graded Khovanov-Rozansky homology of $T_{m,n}$ by considering a certain filtration on $\mathrm{L}_{\frac{m}{n}}$. In this paper, we show that two of the proposed candidates, the algebraic filtration and the inductive filtration, are equal. |
| title | Rational Cherednik Algebras and Torus Knot Invariants |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2402.18770 |