2010 Fiscal Year Final Research Report
Induction and restriction of representations
| Project/Area Number |
20540194
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kinki University |
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Principal Investigator |
FUJIWARA Hidenori Kinki University, 産業理工学部, 教授 (50108643)
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| Research Collaborator |
ALI Baklouti SFAX大学(TUNISIA), 理学部, 教授
JEAN Ludwig METZ大学(FRANCE), 理学部, 教授
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| Project Period (FY) |
2008 – 2010
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| Keywords | リー群 / 可解リー群 / 冪零リー群 / ユニタリ表現 / 軌道の方法 / Plancherel公式 / 誘導表現 / 既約分解 |
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| Research Abstract |
In a field of pure mathematics called representation theory of Lie groups, I carried out for exponential solvable Lie groups, where the exponential map is a diffeomorphism from Lie algebra onto Lie group, a research related to the irreducible decomposition of induced representation from a 1-dimensional unitary character of a subgroup (monomial representation) and obtained the following results.
1. If the multiplicity of a monomial representation in its irreducible decomposition is of discrete type, we could describe explicitly its Plancherel formula and show the commutativity of the associated algebra of invariant differential operators. We also found a negative example on a certain problem of Duflo.
2. Gathering the results obtained until now by Grants-in-Aid for Scientific Research, I published a research book entitled "Unitary representations of exponential solvable Lie groups"(Sugaku-shobo, 2010, 352 pages).
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