2001 Fiscal Year Final Research Report Summary
Research on the representations of cyclotomic Hecke algebras and finite algebraic groups of classical type
| Project/Area Number |
12640016
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Tokyo University of Mercantile Marine |
|---|
Principal Investigator |
ARIKI Susumu Tokyo University of Mercantile Marine, 商船学部, 助教授 (40212641)
|
|---|
| Project Period (FY) |
2000 – 2001
|
| Keywords | finite representation type / Hecke algebra / decomposition numbers / Fock space / crystal basis / canonical basis |
|---|
| Research Abstract |
We have determined when a Hecke algebra has finite representation type. In classical types, the case where the Hecke algebra has type B is essential, and the result in this case is based on the theory which I explained in my book published in 2000, in the project term (Exceptional types were settled by Hyoue Miyachi)
More precisely, using Morita equivalence theorem of Dipper and Mathas the proof is reduced to the case where a two-parameter Hecke algebra of type B has 1 and q^f as the parameters. Then we obtain certain decomposition numbers by the computation of some canonical basis elements. We combine this with Specht module theory and the theory of Artinian algebras. As a result we have a necessary and sufficient condition n<min (e, 2f+4, 2e-2f+4) where q is a primitive eth root of unity. Results for Hecke algebros of classical type are obtained as a Corollary of this result. Related to this project, I also published papers one on the result that λ : Kleshchev<->D^λ*0 the other on combinatorios and crystal.
Moreover, I've completed the English translation of the book mentioned above. This will be published by the American Mathematical Society.
|
