From Cherednik algebras to knot homology via cuspidal D-modules
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910508766986240 |
|---|---|
| author | Ma, Xinchun |
| author_facet | Ma, Xinchun |
| contents | We show that the triply-graded Khovanov-Rozansky homology of the $(m,n)$ torus knot can be recovered from the finite-dimensional representation $\mathrm{L}_{m/n}$ of the rational Cherednik algebra at slope $m/n$, endowed with the Hodge filtration coming from the cuspidal character D-module. Our approach involves expressing the associated graded of the cuspidal character D-module in terms of a dg module closely related to the action of the shuffle algebra on the equivariant K-theory of the Hilbert scheme of points on the plane, thereby proving the rational master conjecture. As a corollary, we identify the Hodge filtration with the inductive and algebraic filtrations on $\mathrm{L}_{m/n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00971 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From Cherednik algebras to knot homology via cuspidal D-modules Ma, Xinchun Representation Theory Algebraic Geometry Combinatorics Quantum Algebra We show that the triply-graded Khovanov-Rozansky homology of the $(m,n)$ torus knot can be recovered from the finite-dimensional representation $\mathrm{L}_{m/n}$ of the rational Cherednik algebra at slope $m/n$, endowed with the Hodge filtration coming from the cuspidal character D-module. Our approach involves expressing the associated graded of the cuspidal character D-module in terms of a dg module closely related to the action of the shuffle algebra on the equivariant K-theory of the Hilbert scheme of points on the plane, thereby proving the rational master conjecture. As a corollary, we identify the Hodge filtration with the inductive and algebraic filtrations on $\mathrm{L}_{m/n}$. |
| title | From Cherednik algebras to knot homology via cuspidal D-modules |
| topic | Representation Theory Algebraic Geometry Combinatorics Quantum Algebra |
| url | https://arxiv.org/abs/2407.00971 |