Schubert geometry and special polynomials
| Project/Area Number |
20540053
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Okayama University of Science |
|---|
Principal Investigator |
IKEDA Takeshi Okayama University of Science, 理学部, 准教授 (40309539)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
NARUSE Hiroshi 岡山大学, 教育学部, 教授 (20172596)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
OHMOTO Toru 北海道大学, 大学院・理学研究院, 准教授 (20264400)
NAKAGAWA Masaki 香川高等専門学校, 講師 (50370036)
|
|---|
| Project Period (FY) |
2008 – 2010
|
| Project Status |
Completed (Fiscal Year 2010)
|
| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| Keywords | シューベルト類 / 同変コホモロジー / 特殊多項式 / 旗多様体 / グラスマン多様体 / ピエリ型公式 / 超対称多項式 / 同変K理論 / シューベルト幾何 / 集合値shifted tableau / Schubert幾何 / コホモロジー / Schur関数 |
|---|
| Research Abstract |
For the flag variety of classical Lie groups, we introduced special polynomials representing the Schubert classes in torus equivariant cohomology ring. We established some fundamental properties for these polynomials. In order to extend this result to torus equivariant K-theory, we introduced special family of polynomials (K-theoretic Q-and P-functions) representing the Schubert classes in the torus equivariant K-theory of classical Grassmannian varieties. We also developed combinatorics of these polynomials. In particular, we discussed a relationship to excited Young diagrams and shifted set-valued tableaux. We introduced a Robinson-Schensted type algorithm for these tableaux. As an application of this algorithm, we proved Pieri type formulas for the K-theoretic Q-functions.
|
Report
(4 results)
Research Products
(52 results)
