2022 Fiscal Year Final Research Report
Special functions and combinatorics arising from parametric deformations of representation-theoretical structures
| Project/Area Number |
18K03248
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Review Section |
Basic Section 11010:Algebra-related
|
|---|
| Research Institution | University of the Ryukyus |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2018-04-01 – 2023-03-31
|
| Keywords | 表現論 / 組合せ論 / 整数論 / パラメタ変形 |
|---|
| Outline of Final Research Achievements |
We have focused on determinants and harmonic oscillators and their deformation by parameters.
Regarding the former, we have studied the followings: concrete calculations on the known result of the multiplicities in the irreducible decomposition of the plethysms by a new approach, the spectrum of the analog of the Cayley graph determined by pairs of finite groups and their subgroups, the description and applications of representation-theoretic and combinatorial objects brought by the parameter deformation of determinants and the relative invariants derived from them.
In the latter, we have studied the followings: parameter deformations of harmonic oscillators, including the structure of special values of their spectral zeta functions and the generalization of the automorphic integrals arising from them, eigenvalue degeneration in parameter deformations of closely related interaction models, and supercongruences satisfied by the Apery-like numbers.
|
| Free Research Field |
表現論
|
| Academic Significance and Societal Importance of the Research Achievements |
行列式や調和振動子といった具体的対象の場合について、「対称性の高い数学的対象」のパラメタ変形がもたらす「対称性の崩れを表す量」は数学的に興味深い対象となるだろうという作業仮説的期待を支持するような結果およびそこからの広がりに関する知見を積み重ねることが出来た。
|
