| 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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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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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 / Terwilliger 代数 / ＴＤ 対 / Ｌ対 / PかつQ多項式スキーム / Terwilliger algebra / quantum affine algebra / augmented TD-algebra / P かつ Q-多項式スキーム / Drinfel'd polynomial |
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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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