2013 Fiscal Year Final Research Report
A study of q-analogues of symmetric spaces in the framework of association schemes
| Project/Area Number |
23654005
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Kanazawa University |
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Principal Investigator |
ITO Tatsuro 金沢大学, 数物科学系, 教授 (90015909)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 離散的対称空間 / ＰかつＱ多項式スキーム / Bose-Mesner代数 / Terwilliger代数 / Ｌeonard対 / Ｔridiagonal対 / Askey-Wilson多項式 / アフィン量子群 |
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| Research Abstract |
It is conjectured about the Terwilliger algebras of P- and Q-polynomoial schemes that a character formula holds for their irreducible representations, and in turn that their irreducible representations have a structure that corresponds to the decomposition of the character formula. This conjecture was known to be true for the case of type I and left open for the remaining cases, i.e., the cases of type II, III. In this study, we have settled the conjecture affirmatively by showing TD-pairs of type II, III are certain kind of tensor products of L-pairs. As a result, it is shown that a character formula holds not only for TD-pairs of type I, but also for those of type II, III.
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