2016 Fiscal Year Final Research Report
Study of 2-representations and its applications to Broue's conjecture
| Project/Area Number |
26800005
|
|---|
| Research Category |
Grant-in-Aid for Young Scientists (B)
|
| Allocation Type | Multi-year Fund |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | The University of Tokyo |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2014-04-01 – 2017-03-31
|
| Keywords | 量子群 / 柏原クリスタル / アフィン・リー環 / 対称群 / スピン表現 / 圏論化 / ロジャーズ・ラマヌジャン恒等式 / 整数の分割 |
|---|
| Outline of Final Research Achievements |
In a course of a study of spin analog of K\"ulshammer-Olsson-Robinson theory (Invent.Math.,(2003)), we found and proved a new Rogers-Ramajujan type identity for each odd number $p\geq 3$ (joint work with Masaki Watanabe). When $p=3$, it is nothing but ``Schur partition theorem (1926)'' that you can find in almost all textbooks on the theory of partitions. When $p=5$, it is the same as the conjecture due to G.Andrews found in 1970s in a course of his 3 parameter generalization of the Rogers-Ramajujan identities. Andrews' conjecture was proved about 20 years later (Trans.A.M.S.,(1994)) with an aid of computers. Our generalization and proof are based on a theory of perfect crystals of Kyoto school and provides new insight into the theory of partitions (arXiv:1609.01905).
|
| Free Research Field |
代数学
|
