Moduli theory and quantum algebras
| Project/Area Number |
25800014
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Kyoto University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2013-04-01 – 2016-03-31
|
| Project Status |
Completed (Fiscal Year 2015)
|
| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
|---|
| Keywords | 量子代数 / モジュライ空間 / 幾何学的表現論 / 変形W代数 / Hall代数 / Ding-Iohara-Miki代数 / 頂点代数 |
|---|
| Outline of Final Research Achievements |
We studied the quantum symmetry of the moduli spaces, focusing on the AGT relations and its K-theoretic/difference analogue.
We achieved some explicit formulas on the quantum algebras such as quantum toroidal algebras and deformed W-algebras.
We also studied the Ringel-Hall algebra, its Drinfeld double and Bridgeland-Hall algebra of two-periodic complexes, particularly focusing on the case of coherent sheaves over a curve.
|
Report
(4 results)
Research Products
(29 results)
