2013 Fiscal Year Final Research Report
Representation theory and combinatorics of classical groups, quantum groups and Hecke algebras
| Project/Area Number |
23540008
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
TERADA Itaru 東京大学, 数理(科)学研究科(研究院), 准教授 (70180081)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
OKADA Soichi 名古屋大学, 大学院・多元数理科学研究科, 教授 (20224016)
|
|---|
| Project Period (FY) |
2011 – 2013
|
| Keywords | リトルウッド・リチャードソン盤 / ヤング図形 / 組合せ論 / 全単射 / 対合性 / ロビンソン・シェンステッド対応 / 旗多様体 / ハイブ |
|---|
| Research Abstract |
Littlewood-Richardson coefficients, which are the coefficients of products of Schur functions expanded as sums of Schur functions, are described as the numbers of combinatorial objects called Littlewood-Richardson tableaux.
For the bijection between Littlewood-Richardson tableaux given by Azenhas, which realizes the symmetry of Littlewood-Richardson coefficients reflecting the commutativity of Schur dunctions, is given two combinatorial proofs, by collaboration with King and Azenhas, one of which using the conventional Littlewood-Richardson tableaux and the other using new combinatorial objects called hives which have been introduced by Knutson and Tao rather recently.
|
