{"created":"2023-06-20T16:34:03.006081+00:00","id":3132,"links":{},"metadata":{"_buckets":{"deposit":"134535ac-e7b7-4947-abd0-f402db1ce03b"},"_deposit":{"created_by":3,"id":"3132","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"3132"},"status":"published"},"_oai":{"id":"oai:kindai.repo.nii.ac.jp:00003132","sets":["14:2667:2689:2693","21:2669:2691:2694"]},"author_link":["3463","3464","3465"],"item_8_alternative_title_3":{"attribute_name":"その他(別言語等)のタイトル","attribute_value_mlt":[{"subitem_alternative_title":"Induction and restriction of representations"}]},"item_8_biblio_info_21":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2010-01-01","bibliographicIssueDateType":"Issued"},"bibliographicPageEnd":"4","bibliographicPageStart":"1","bibliographic_titles":[{"bibliographic_title":"科学研究費補助金研究成果報告書 (2010. )"}]}]},"item_8_description_33":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"研究成果の概要(和文):純粋数学の1分野であるリー群の表現論において、リー環からリー群への指数写像が微分同相写像となるような指数型可解リー群に対して、部分群の1次元ユニタリ指標から誘導されるユニタリ表現(単項表現)の既約表現への分解に関連する研究を行い、以下の成果を得た。 1.指数型可解リー群の単項表現の既約分解における重複度が離散的ならば、そのプランシュレル公式を具体的に記述することができ、関連する不変微分作用素環の可換性を示すことができた。また、この可換性に関して Duflo 氏のある問題について否定的な例を見つけた。 2.これまでの科学研究費補助金による研究成果をまとめて研究図書「指数型可解リー群のユニタリ表現」(数学書房、平成22 年刊行、352 ページ)を出版した。 研究成果の概要(英文):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”(Sûgaku-shobô, 2010, 352 pages).","subitem_description_type":"Abstract"}]},"item_8_description_36":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究種目:基盤研究(C); 研究期間:2008~2010; 課題番号:20540194; 研究分野:表現論; 科研費の分科・細目:数学・基礎解析学","subitem_description_type":"Other"}]},"item_8_description_37":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"subitem_description":"Research Paper","subitem_description_type":"Other"}]},"item_8_description_41":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_8_publisher_14":{"attribute_name":"出版者 名前","attribute_value_mlt":[{"subitem_publisher":"近畿大学"}]},"item_8_relation_11":{"attribute_name":"著者 外部リンク","attribute_value_mlt":[{"subitem_relation_name":[{"subitem_relation_name_text":"https://kaken.nii.ac.jp/ja/r/50108643"}]}]},"item_8_text_10":{"attribute_name":"著者 役割","attribute_value_mlt":[{"subitem_text_value":"研究代表者"},{"subitem_text_value":"研究協力者"},{"subitem_text_value":"研究協力者"}]},"item_8_text_7":{"attribute_name":"著者(英)","attribute_value_mlt":[{"subitem_text_language":"en","subitem_text_value":"FUJIWARA, HIDENORI"}]},"item_8_text_8":{"attribute_name":"著者 所属","attribute_value_mlt":[{"subitem_text_value":"近畿大学産業理工学部; 教授"},{"subitem_text_value":"SFAX 大学"},{"subitem_text_value":"METZ 大学"}]},"item_8_version_type_12":{"attribute_name":"版","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"藤原, 英徳"},{"creatorName":"フジワラ, ヒデノリ","creatorNameLang":"ja-Kana"}],"nameIdentifiers":[{},{}]},{"creatorNames":[{"creatorName":"BAKLOUTI, ALI"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"LUDWIG, JEAN"}],"nameIdentifiers":[{}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2016-02-17"}],"displaytype":"detail","filename":"KAKEN_20540194seika.pdf","filesize":[{"value":"31.3 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"KAKEN_20540194seika.pdf","url":"https://kindai.repo.nii.ac.jp/record/3132/files/KAKEN_20540194seika.pdf"},"version_id":"bd3e076a-579c-421e-8bfb-9733f1ad5a8e"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"リー群","subitem_subject_scheme":"Other"},{"subitem_subject":"可解リー群","subitem_subject_scheme":"Other"},{"subitem_subject":"冪零リー群","subitem_subject_scheme":"Other"},{"subitem_subject":"ユニタリ表現","subitem_subject_scheme":"Other"},{"subitem_subject":"軌道の方法","subitem_subject_scheme":"Other"},{"subitem_subject":"Plancherel公式","subitem_subject_scheme":"Other"},{"subitem_subject":"誘導表現","subitem_subject_scheme":"Other"},{"subitem_subject":"既約分解","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"表現の誘導と制限","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"表現の誘導と制限"}]},"item_type_id":"8","owner":"3","path":["2693","2694"],"pubdate":{"attribute_name":"公開日","attribute_value":"2011-07-08"},"publish_date":"2011-07-08","publish_status":"0","recid":"3132","relation_version_is_last":true,"title":["表現の誘導と制限"],"weko_creator_id":"3","weko_shared_id":-1},"updated":"2023-06-21T01:45:37.274880+00:00"}