Updated on 2025/03/26

写真a

 
MIYACHI Hyoue
 
Organization
Graduate School of Science Department of Mathematics Professor
School of Science Department of Mathematics
Title
Professor
Affiliation
Institute of Science

Position

  • Graduate School of Science Department of Mathematics 

    Professor  2023.04 - Now

  • Graduate School of Science Department of Mathematics 

    Associate Professor  2022.04 - 2023.03

  • School of Science Department of Mathematics 

    Professor  2023.04 - Now

  • School of Science Department of Mathematics 

    Associate Professor  2022.04 - 2023.03

Research Areas

  • Natural Science / Algebra

Research Interests

  • Kazhdan-Lusztig polynomials

  • Rational double affine Hecke algebras

  • Representation Theory of Algebraic Groups and Quantum Groups

  • 代数群と量子群の表現論

Committee Memberships (off-campus)

  • 日本数学コンクール実行委員   日本数学コンクール  

    2022.04 - Now 

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    作問、採点。

Job Career (off-campus)

  • Osaka Metropolitan University

    2022.04 - Now

Papers

  • On the Mackey formulas for cyclotomic Hecke algebras and categories O of rational Cherednik algebras Reviewed

    KUWABRA Toshiro,MIYACHI Hyohe,WADA Kentaro

    Osaka J. Math.   58 ( 1 )   103 - 134   2021.01

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    Publishing type：Research paper (scientific journal)   Kind of work：Joint Work  

  • Parallelotope tilings and q-decomposition numbers Reviewed

    Chuang Joseph, Miyachi Hyohe, Tan Kai Meng

    ADVANCES IN MATHEMATICS   321   80 - 159   2017.12（ ISSN:0001-8708 ）

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    Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.aim.2017.09.024

  • Decomposition matrices for d-Harish-Chandra series: the exceptional rank two cases Reviewed

    M. Chlouveraki & H. Miyachi

    LMS J. Comput. Math.   14   271 - 290   2011

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    Publishing type：Research paper (scientific journal)   Kind of work：Single Work  

  • Runner removal Morita equivalences Reviewed

    J. Chuang & H. Miyachi

    Progr. Math. Birkhäuser/Springer, New York   ( 284 )   55 - 79   2010

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    Publishing type：Research paper (scientific journal)   Kind of work：Single Work  

  • Module Correspondences in Rouquier Blocks of Finite General Linear Groups(3)

    Akihiko Hida, Hyohe Miyachi

    BIRKHAUSER VERLAG AG　REPRESENTATION THEORY OF ALGEBRAIC GROUPS AND QUANTUM GROUPS   284 ( 284 )   81 - 92   2010（ ISSN:0743-1643 ）

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    In this chapter we shall consider l-modular represenations of finite general linear groups in non-defining characteristic l > 0. We focus the nicest l-block algebras in this representation theory, which are also known as unipotent Rouquier blocks.
    Let B(w,rho) be the unipotent l-block algebra of a general linear group over the finite field with q elements associated with an e-weight w > 0 and a Rouquier e-core rho with respect to w where e is the multiplicative order of q modulo l > 0. (See the second paragraph of Sect. A for the definition of rho.)
    We assume that B(w,p) has an abelian defect, ie, l > w. It is known that there exists a Morita equivalence F between B(w,rho) and the wreath product block B1,(sic). This result is obtained by W. Turner and the second author independently. The both methods are completely identical each other and are very similar to J. Chuang and R. Kessar's method on symmetric groups.
    R. Kessar's method on symmetric groups.
    In this chapter, under the equivalence F we shall determine the explicit correspondences of the simple, the Young and the Specht modules over the Rouquier block B(w,p) and the local subgroup block B(sic). The result is used to prove the intial condition of runner removal Morita equivalence theorem.

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Books and Other Publications

MISC

  • $v$-ANALOGUES OF KLESHCHEV BRANCHING COEFFICIENTS AND DECOMPOSITION NUMBERS

    MIYACHI Hyohe

    1438   1 - 18   2005.07

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  • SOME DEGENERATE UNIPOTENT BLOCKS

    MIYACHI Hyohe

    1375   119 - 123   2004.02

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  • $F_4$型HECKE環のブロックについて

    宮地 兵衛

    数理解析研究所講究録   1382   171 - 188   2004

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  • $GL_n(F_q)$のブロックにおける圏同値の組合わせ論的記述,$q$との独立性と分解定数について

    宮地 兵衛

    数理解析研究所講究録   1190   35 - 49   2001.02

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  • ON THE PRINCIPAL BLOCKS OF FINITE GENERAL LINEAR GROUPS IN NON-DEFINING CHARACTERISTIC

    飛田, 明彦, 宮地 兵衛

    数理解析研究所講究録   1140   127 - 130   2000.04

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Presentations

  • A survey on the derived categories of module categories over Schur algebras Invited International conference

    Hyohe Miyachi

    Derived categories and cotilting theory: conference honoring Jun-ichi Miyachi on the occasion of his 65th birthday  2024.09  Hiroki Abe (Tokyo Keizai University) Takuma Aihara (Tokyo Gakugei University) Hideto Asashiba (Shizuoka University) Ayako Itaba (Tokyo University of Science) Osamu Iyama (The University of Tokyo) Hiroshi Nagase (Tokyo Gakugei University)

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    Presentation type：Oral presentation (invited, special)  

    Venue：Tokyo Gakugei University  

  • On two reciprocities of Hecke algebras

    Hyohe Miyachi

    Cohomology theory of finite groups and related topics  2024.02  Akihiko Hida

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    Presentation type：Oral presentation (general)  

    Venue：RIMS, Kyoto University  

  • On Two Reciprocities on Hecke Algebras International conference

    Hyohe Miyachi

    2023.10  N. Fujita, G. Ikeda

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    Presentation type：Oral presentation (general)  

    Venue：Waseda University  

  • On the Mackey formula for Hecke algebras associated with the complex reflection group of type G(r,1,n) International conference

    MIYACHI Hyohe

    On the Mackey formula for Hecke algebras associated with the complex reflection group of type G(r,1,n)  2019.08 

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    Presentation type：Oral presentation (general)  

  • On the Mackey formula for Hecke algebras and GGOR category O Invited International conference

    Hyohe MIYACHI

    Workshop on Representation Theory of Symmetric Groups and Related Algebras  2017.12 

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    Presentation type：Oral presentation (general)  

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Works

  • 平成20年度RIMS研究集会「組合せ論的表現論の拡がり」 主催・講究録作成

    2008

  • 一般線型群のモジュラー表現論

    2007

  • 書評:岡田聡一, 古典群の表現論と組み合わせ論(上・下)

    2007

  • 第７回代数群と量子群の表現論 研究集会主催／報告集作成

    2004

Acceptance of Researcher

  • 2024  Number of researchers：2

  • 2023  Number of researchers：2

Charge of on-campus class subject

  • 数学特別研究2A

    2024   Intensive lecture   Graduate school

  • 数学特別研究1A

    2024   Intensive lecture   Graduate school

  • 数理構造論演習1

    2024   Intensive lecture   Graduate school

  • 数学特別研究5A

    2024   Intensive lecture   Graduate school

  • 数学特別研究4A

    2024   Intensive lecture   Graduate school

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Charge of off-campus class subject

  • 代数学I

    Institution：Osaka City University

  • 代数学II

    Institution：Osaka City University

  • 代数学III

    Institution：Osaka City University

  • 代数学IV

    Institution：Osaka City University

  • 代数学講義I

    Institution：Osaka City University

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Faculty development activities

  • 数学FD meeting  2024

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    数学に関する国際基幹教育科目の情報共有のための勉強会。

Number of instructed thesis, researches

  • 2024

    Number of instructed the graduation thesis：2  Number of graduation thesis reviews：2

    [Number of instructed the Master's Program] (previous term)：0  [Number of instructed the Master's Program] (letter term)：0

    [Number of master's thesis reviews] (chief)：1  [Number of master's thesis reviews] (vice-chief)：2

    [Number of doctoral thesis reviews] (chief)：1  [Number of doctoral thesis reviews] (vice-chief)：0

  • 2023

    Number of instructed the graduation thesis：1  Number of graduation thesis reviews：2

    [Number of instructed the Master's Program] (previous term)：1  [Number of instructed the Master's Program] (letter term)：0

    [Number of master's thesis reviews] (chief)：1  [Number of master's thesis reviews] (vice-chief)：1

    [Number of doctoral thesis reviews] (chief)：0  [Number of doctoral thesis reviews] (vice-chief)：0

Original item・Special report (Education Activity)

  • 2023

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    Original item：博士前期課程学生成績。

    Special report：指導する博士前期課程学生が理学研究科総代となった。

Social Activities　⇒ Link to the list of Social Activities

  • 日本数学コンクール

    Role(s)： Lecturer,　Consultant,　Official expert,　Planner,　Logistic support

    Type： Seminar, workshop

    名古屋大学大学院多元数理科学研究科および大阪公立大学数学研究所  日本数学コンクール  2022.04 - Now

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    SDGs：

    Audience： Junior high school students,　High school students

    作問、採点、解説を担当。

Foreigner acceptance

  • 2024

    foreigners accepted :1

    International Students :0

International exchange activities

  • サイエンスフロンティア科目を中心に本学大学院生の教育をBernard Leclerc氏に行ってもらった。

    Field category :Education

    Country name :République française   2024.10 - 2024.11

  • 大阪公立大学国際招へい事業によりBernard Leclerc教授を招へいした。柏原結晶基底に関する共同研究を行った。

    Field category :Research

    Country name :République française   2024.10 - 2024.11

  • I stayed in City University, London. J. Chuang, K.M. Tan and myself did a joint research.

    Field category :Research

    Country name :United Kingdom of Great Britain and Northern Ireland   2023.05