Updated on 2024/04/10

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

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。

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  

  • 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.

  • Module correspondences in Rouquier blocks of finite general linear groups Reviewed

    A. Hida & H. Miyachi

    Progr. Math. Birkhäuser/Springer, New York   ( 284 )   81 - 92   2010

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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  

  • Uno's conjecture for the exceptional Hecke algebras Reviewed

    H. Miyachi

    RIMS Kôkyûroku Bessatsu B11: New Trends in Combinatorial Representation Theory   11   155 - 178   2009

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

  • Kleshchev's decomposition numbers and branching coefficients in the Fock space Reviewed

    CHUANG J, MIYACHI H, TAN Km

    Trans. Amer. Math. Soc.   360 ( 3 )   1179 - 1191   2008（ ISSN:0002-9947 ）

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

    DOI： 10.1090/S0002-9947-07-04202-X

    J-GLOBAL

  • Rouquier blocks in Chevalley groups of type E Reviewed

    MIYACHI H

    Adv. Math.   217 ( 6 )   2841 - 2871   2008（ ISSN:0001-8708|1090-2082 ）

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

    DOI： 10.1016/j.aim.2007.12.004

    J-GLOBAL

  • A v-analogue of Peel's theorem Reviewed

    J. Chuang & H. Miyachi & K.M. Tan

    Journal of Algebra   280   219 - 231   2004

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

    DOI： 10.1016/j.jalgebra.2004.04.017

  • Constructible characters and canonical bases Reviewed

    B. Leclerc & H. Miyachi

    Journal of Algebra   277   298 - 317   2004

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

    DOI： 10.1016/j.jalgebra.2004.02.023

  • Row and column removal in the q-deformed Fock space Reviewed

    J. Chuang & H. Miyachi & K.M. Tan

    Journal of Algebra   254   84 - 91   2002

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

    DOI： 10.1016/S0021-8693(02)00062-5

  • Some closed formulas for canonical bases of Fock spaces Reviewed

    B. Leclerc & H. Miyachi

    American Mathematical Society Representation Theory   6   290 - 312   2002

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

  • Donovan conjecture and Loewy length for principal 3-blocks of finite groups with elementary abelian Sylow 3-subgroups of order 9 Reviewed

    Communication in Algebra   29 ( 10 )   4509 - 4522   2001

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

    DOI： 10.1081/AGB-100106771

  • The Unipotent Blocks of Finite General Linear Groups in Non-defining Characteristic Reviewed

    学位論文（千葉大学）   1   2001

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

  • The principal 3-blocks of four- and five-dimensional projective special linear groups in non-defining characteristic

    S Koshitani, H Miyachi

    ACADEMIC PRESS INC ELSEVIER SCIENCE　JOURNAL OF ALGEBRA   226 ( 2 )   788 - 806   2000.04（ ISSN:0021-8693 ）

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    In representation theory of finite groups, there is a well-known and important conjecture due to M. Broue. He has conjectured that, for any prime p, if a finite group G has an abelian Sylow p-subgroup P, then the principal p-blocks of G and the normalizer N(G)(P) of P in G are derived equivalent. Let q be a power of a prime such that q = 2 or 5 (mod 9), In this paper we show that Broue's conjecture is true for p = 3 and for G = PSL(4)(q) and G = PSL(5)(q). In these cases, G has elementary abelian Sylow 3-subgroups of order 9. What we prove here is the following. In the case G = PSL(4)(q) all the principal 3-blocks of G are Morita (even Puig) equivalent independently of infinitely many q. In the case G = PSL(5)(q) all the principal 3-blocks of G are Morita (even Puig) equivalent to the principal 3-block of N(G)(P) independently of infinitely many q. (C) 2000 Academic Press.

    DOI： 10.1006/jabr.1999.8167

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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

  • 一般線型群のモジュラー表現について

    宮地 兵衛

    数理解析研究所講究録   1057   88 - 102   1998.09

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Presentations

  • 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)  

  • Cuspidal modules over Rational Cherednik algebras and finite Chevalley groups Invited International conference

    Hyohe MIYACHI

    The 3rd International Symposium on Groups, Algebras and Related Topics, the 50th anniversary of the “Journal of Algebra”  2013.06 

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    Presentation type：Oral presentation (general)  

  • Rational Cherednik algebras and finite Chevalley groups in characteristic l>0 Invited International conference

    Hyohe MIYACHI

    Modular Representation Theory of Finite and p-adic Groups  2013.04 

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    Presentation type：Oral presentation (general)  

  • 一般線型群のモジュラー表現の圏の比較 Invited Domestic conference

    宮地　兵衛

    日本数学会秋季総合分科会 特別講演  2012.09 

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    Presentation type：Oral presentation (invited, special)  

  • Hidden Hecke Algebras and duality Invited International conference

    Hyohe MIYACHI

    Shanghai Workshop on Representation Theory  2010.12 

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    Presentation type：Oral presentation (general)  

  • Hidden Hecke Algebras and Duality Invited International conference

    Hyohe MIYACHI

    The 10-th International Conference by Graduate School of Nagoya University “Representation Theory of Algebraic Groups and Quantum Groups ’10 “  2010.08 

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    Presentation type：Oral presentation (general)  

  • Runner removal Morita equivalences International conference

    Hyohe MIYACHI

    The 6-th International Conference by Graduate School of Nagoya University, “Representation Theory of Algebraic Groups and Quantum Groups ’ 06”  2006.06 

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    Presentation type：Oral presentation (general)  

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Acceptance of Researcher

  • 2023  Number of researchers：2

Charge of on-campus class subject

  • 数理構造論ゼミナール

    2023   Intensive lecture   Graduate school

  • 数理構造論演習2

    2023   Intensive lecture   Graduate school

  • 数理構造論演習1

    2023   Intensive lecture   Graduate school

  • 特別研究

    2023   Intensive lecture   Undergraduate

  • 代数学Ⅲ演習

    2023   Weekly class   Undergraduate

  • 代数学Ⅲ

    2023   Weekly class   Undergraduate

  • 微積分2

    2023   Weekly class   Graduate school

  • 基礎数学B

    2023   Weekly class   Graduate school

  • 後期海外特別研究２

    2023   Intensive lecture   Graduate school

  • 数理構造論演習1

    2023   Intensive lecture   Graduate school

  • 数理科学A

    2023   Weekly class   Graduate school

  • 数学特別研究1A

    2022   Intensive lecture   Graduate school

  • 数理科学A

    2022   Weekly class   Graduate school

  • 数学概論Ⅱ

    2022   Weekly class   Graduate school

  • 代数学Ⅰ演習

    2022   Weekly class   Undergraduate

  • 代数学Ⅰ

    2022   Weekly class   Undergraduate

  • 数理構造論ゼミナールA

    2022   Intensive lecture   Graduate school

  • 数理構造論演習1

    2022   Intensive lecture   Graduate school

  • 数理構造論演習（M２）

    2022   Intensive lecture   Graduate school

  • 数理構造論ゼミナール

    2022   Intensive lecture   Graduate school

  • 数学概論B

    2022     Graduate school

  • 基礎数学B/必:経,選:商<商･公>1(市大:CE1a)S

    2022   Weekly class   Graduate school

  • 微積分2/必:理〈物理〉S

    2022   Weekly class   Graduate school

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Number of instructed thesis, researches

  • 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

  • 日本数学コンクール

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

    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

    Type：Seminar, workshop

    作問、採点、解説を担当。

International exchange activities

  • 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