Characteristic cycles of standard modules for the rational Cherednik algebra of type Z/lZ
| dc.creator | Kuwabara, Toshiro | |
| dc.date | 2008-01-27 | |
| dc.date.accessioned | 2026-07-07T08:56:45Z | |
| dc.date.available | 2026-07-07T08:56:45Z | |
| dc.description | We study the representation theory of the rational Cherednik algebra $H_κ= H_κ({\mathbb Z}_l)$ for the cyclic group ${\mathbb Z}_l = {\mathbb Z} / l {\mathbb Z}$ and its connection with the geometry of the quiver variety $M_θ(δ)$ of type $A_{l-1}^{(1)}$. We consider a functor between the categories of $H_κ$-modules with different parameters, called the shift functor, and give the condition when it is an equivalence of categories. We also consider a functor from the category of $H_κ$-modules with good filtration to the category of coherent sheaves on $M_θ(δ)$. We prove that the image of the regular representation of $H_κ$ by this functor is the tautological bundle on $M_θ(δ)$. As a corollary, we determine the characteristic cycles of the standard modules. It gives an affirmative answer to a conjecture given in [Gordon, arXiv:math/0703150v1] in the case of ${\mathbb Z}_l$. | |
| dc.description | 40 pages, To appear in J. Math. Kyoto Univ | |
| dc.identifier | https://arxiv.org/abs/0801.4136 | |
| dc.identifier | http://arxiv.org/abs/0801.4136 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/146721 | |
| dc.subject | Representation Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 16G99, 14J60, | |
| dc.title | Characteristic cycles of standard modules for the rational Cherednik algebra of type Z/lZ | |
| dc.type | text |