• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Integrated study of probability and representation theory towards harmonic analysis on huge groups

Research Project

Project/Area Number 19340032
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionNagoya University

Principal Investigator

HORA Akihito  Nagoya University, 大学院・多元数理科学研究科, 教授 (10212200)

Co-Investigator(Kenkyū-buntansha) OKADA Soichi  名古屋大学, 大学院・多元数理科学研究科, 教授 (20224016)
TATE Tatsuya  名古屋大学, 大学院・多元数理科学研究科, 准教授 (00317299)
HIRAI Takeshi  京都大学, 名誉教授 (70025310)
OBATA Nobuaki  東北大学, 大学院・情報科学研究科, 教授 (10169360)
SHIMOMURA Hiroaki  高知大学, 教育学部, 教授 (20092827)
KAWAZOE Takeshi  慶應義塾大学, 総合政策学部, 教授 (90152959)
YAMADA Hirofumi  岡山大学, 大学院・自然科学研究科, 教授 (40192794)
ARAI Hitoshi  東京大学, 大学院・数理科学研究科, 教授 (10175953)
NISHIYAMA Kyo  京都大学, 大学院・理学研究科, 准教授 (70183085)
ISHI Hideyuki  名古屋大学, 大学院・多元数理科学研究科, 准教授 (00326068)
Co-Investigator(Renkei-kenkyūsha) MATSUMOTO Sho  名古屋大学, 大学院・多元数理科学研究科, 助教 (60547553)
INAHAMA Yuzuru  名古屋大学, 大学院・多元数理科学研究科, 准教授 (80431998)
Project Period (FY) 2007 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000)
Fiscal Year 2010: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2009: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2008: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2007: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Keywords解析学 / 関数解析学 / 確率論 / 表現論 / 調和解析 / 表現の指標 / 対称群 / ヤンググラフ / 環積 / 無限対称群 / 漸近挙動 / 指標 / 量子確率論
Research Abstract

Towards developing harmonic analysis on huge groups, we did integrated studies of probability theory and group representations. Harmonic analysis is a discipline which seeks deep mathematical structures by looking at symmetries of the objects and develops analysis relying on them. In this study, we are led to huge groups describing the symmetries because our objects are so big as to have an infinite degree of freedom. Main results among the ones we obtained are (i) classification and explicit formulas of the characters which are building blocks of harmonic analysis, and (ii) a series of theorems which construct a bridge between asymptotic behavior of representations of groups and probabilistic limit theorems.

Report

(6 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report   Self-evaluation Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (24 results)

All 2010 2009 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 13 results) Presentation (9 results) Book (1 results) Remarks (1 results)

  • [Journal Article] Towards projective representations and spin characters of finite and infinite complex reflection groups2009

    • Author(s)
      1T.Hirai, E.Hirai, A.Hora
    • Journal Title

      Infinite Dimensional Harmonic Analysis Vol.4

      Pages: 122-128

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T),I.2009

    • Author(s)
      T.Hirai, E.Hira, A.Hora
    • Journal Title

      Nagoya Mathematical Journal Vol.193

      Pages: 1-93

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T), I.2009

    • Author(s)
      T. Hirai, E. Hirai, A. Hora
    • Journal Title

      Nagoya Mathematical Journal 193

      Pages: 1-93

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Towards projective representations and spin characters of finite and infinite complex reflection groups2009

    • Author(s)
      T.Hirai, E.Hirai, A.Hora
    • Journal Title

      Infinite Dimensional Harmonic Analysis Vol. 4

      Pages: 112-128

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limits of characters of wreath products Sn (T) of a compact group T with the symmetric groups and characters of S∞ (T), I.2009

    • Author(s)
      T. Hirai, E. Hirai, A. Hora
    • Journal Title

      Nagoya Mathematical Journal 193

      Pages: 1-93

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T), II.2008

    • Author(s)
      3A.Hora, T.Hirai, E.Hirai
    • Journal Title

      From a viewpoint of probability theory, Journal of Mathematical Society of Japan Vol.60

      Pages: 1187-1217

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic spectral analysis of growing regular graphs2008

    • Author(s)
      Hora, N.Obata
    • Journal Title

      Transactions of American Mathematical Society Vol.360

      Pages: 899-923

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Limits of characters of wreath products Sn(T) of a compact group T with the symmetric groups and characters of S∞(T), II. From a viewpoint of probability theory2008

    • Author(s)
      A. Hora, T. Hirai, E. Hirai
    • Journal Title

      Journal of Mathematical Society of Japan 60

      Pages: 1187-1217

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Asymptotic spectral analysis of growing regular graphs2008

    • Author(s)
      A. Hora, N. Obata
    • Journal Title

      Transactions of American Mathematical Society 360

      Pages: 899-923

    • Related Report
      2009 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] Limits of characters of wreath products Sn (T) of a compact group T with the symmetric groups and characters of S∞ (T), II. From a viewpoint of probability theory2008

    • Author(s)
      A. Hora, T. Hirai, E . Hirai
    • Journal Title

      Journal of Mathematical Society of Japan 60

      Pages: 1187-1217

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic spectral analysis of growing regular graphs2008

    • Author(s)
      A. Hora, N. Obata
    • Journal Title

      Trans. Amer. Math. Soc. 360

      Pages: 899-923

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Characters of wreath products of compact groups with the infinite symmetric group and characters of their canonical subgroups2007

    • Author(s)
      T.Hirai, E.Hirai
    • Journal Title

      Journal of Mathematics of Kyoto University Vol.47

      Pages: 269-320

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Characters of wreath products of compact groups with the infinite symmetric group and characters of their canonical subgroups2007

    • Author(s)
      T. Hirai, E. Hirai
    • Journal Title

      J. Math. Kyoto Univ. 47

      Pages: 269-320

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] Characters and harmonic functions related to infinite wreath product groups2010

    • Author(s)
      A.Hora
    • Organizer
      RIMS Project Research Functions in Number Theory and Their Probabilistic Aspects
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-12-14
    • Related Report
      2010 Final Research Report
  • [Presentation] Characters and harmonic functions related to infinite wreath product groups2010

    • Author(s)
      Akihito Hora
    • Organizer
      RIMS Project Research, Functions in Number Theory and Their Probabilistic Aspects
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-12-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] Kerov's CLT for a non-Plancherel ergodic measures2008

    • Author(s)
      A.Hora
    • Organizer
      無限次元解析と量子確率論
    • Place of Presentation
      東北大学大学院情報科学研究科
    • Year and Date
      2008-11-10
    • Related Report
      2010 Final Research Report
  • [Presentation] Harmonic analysis on symmetric groups and branching graphs2008

    • Author(s)
      A.Hora
    • Organizer
      Non-commutative Harmonic Analysis with Applications to Probability
    • Place of Presentation
      Banach Center, Bedlewo, Poland.
    • Year and Date
      2008-08-22
    • Related Report
      2010 Final Research Report
  • [Presentation] 無限対称群および無限環積群の表現と指標2008

    • Author(s)
      平井武
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-23
    • Related Report
      2010 Final Research Report 2007 Annual Research Report
  • [Presentation] 無限対称群および無限環積群S∞(T)の表現と指標 (函数解析学特別講演)2008

    • Author(s)
      平井武
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-23
    • Related Report
      2009 Self-evaluation Report
  • [Presentation] A strong LLN for some Young diagram ensembles2007

    • Author(s)
      A.Hora
    • Organizer
      Infinite Dimensional Analysis and Quantum Probability
    • Place of Presentation
      Chungbuk National University, Korea
    • Year and Date
      2007-12-03
    • Related Report
      2010 Final Research Report
  • [Presentation] Group characters, random Young diagrams, and some limit theorems2007

    • Author(s)
      A.Hora
    • Organizer
      数論と確率論
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2007-10-15
    • Related Report
      2010 Final Research Report
  • [Presentation] Realization of Vershik-Kerov's type for finite factorial representations of infinite wreath product groups2007

    • Author(s)
      A.Hora
    • Organizer
      Sminarium Dyskretna Analiza Harmoniczna
    • Place of Presentation
      University of Wroclaw, Poland.
    • Year and Date
      2007-06-06
    • Related Report
      2010 Final Research Report
  • [Book] Quantum probability and spectral analysis of graphs2007

    • Author(s)
      A. Hora, N. Obata
    • Total Pages
      389
    • Publisher
      Springer
    • Related Report
      2009 Self-evaluation Report 2007 Annual Research Report
  • [Remarks] ホームページ等

    • Related Report
      2010 Final Research Report

URL: 

Published: 2007-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi