2013 Fiscal Year Final Research Report
New developments of vertex algebra theory
| Project/Area Number |
23654006
|
|---|
| Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | 頂点作用素代数 / D加群 / 変型量子化 / W代数 / アーク空間 |
|---|
| Research Abstract |
(1) We have introduced the notion of an asymptotic algebra of chiral differential operators. We then have constructed, via a chiral Hamiltonian reduction, one such algebra over a resolution of the intersection of the Slodowy slice with the nilpotent cone. We compute the space of global sections of this algebra thereby proving a localization theorem for affine W-algebras at the critical level. This is a joint work with T. Kuwabara and F. Malikov.
(2) We introduced a notion of semi-infinite restriction functor, and shows that it is compatible with admissibility of representations of affine Kac-Moody algebras, enabling an inductive study of Kac-Wakimoto admissible representations.
|
