Updated on 2022/12/04

写真a

 
KITAGAWA, Masatoshi
 
Scopus Paper Info  
Paper Count: 0  Citation Count: 0  h-index: 1

Citation count denotes the number of citations in papers published for a particular year.

Affiliation
Faculty of Education and Integrated Arts and Sciences, School of Education
Job title
Assistant Professor(without tenure)

Concurrent Post

  • Faculty of Education and Integrated Arts and Sciences   Graduate School of Education

Research Experience

  • 2019.04
    -
    Now

    Waseda University   Faculty of Education and Integrated Arts and Sciences School of Education

  • 2017.04
    -
    2019.03

    Nara Women's University   Department of Physics and Mathematics, Faculty of Science

  • 2016.04
    -
    2018.03

    Josai University   Faculty of Sciences, Department of Mathematics

Professional Memberships

  •  
     
     

    THE MATHEMATICAL SOCIETY OF JAPAN

 

Research Areas

  • Algebra

Research Interests

  • リー群

  • 分岐則

  • 表現論

Papers

  • STABILITY OF BRANCHING LAWS FOR HIGHEST WEIGHT MODULES

    Masatoshi Kitagawa

    TRANSFORMATION GROUPS   19 ( 4 ) 1027 - 1050  2014.12  [Refereed]

     View Summary

    In this paper, we study the irreducible decomposition of a (a",[X];G)-module M for a quasi-affine spherical variety X of a connected reductive algebraic group G over a",. We show that for sufficiently large parameters, the decomposition of M with respect to G is reduced to the decomposition of the 'fiber' M/(x (0))M with respect to some reductive subgroup L of G. In particular, we obtain a method to compute the maximum value of multiplicities in M. Our main result is a generalization of earlier work by F. SatAi in [17]. We apply this result to branching laws of holomorphic discrete series representations with respect to symmetric pairs of holomorphic type. We give a necessary and sufficient condition for multiplicity-freeness of the branching laws.

    DOI

    Scopus

  • Stability of branching laws for spherical varieties and highest weight modules

    Masatoshi Kitagawa

    PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES   89 ( 10 ) 144 - 149  2013.12  [Refereed]

     View Summary

    If a locally finite rational representation V of a connected reductive algebraic group G has uniformly bounded multiplicities, the multiplicities may have good properties such as stability. Let X be a quasi-affine spherical G-variety, and M be a (C[X], G)-module. In this paper, we show that the decomposition of M as a G-representation can be controlled by the decomposition of the fiber M/m(x(0))M with respect to some reductive subgroup L subset of G for sufficiently large parameters. As an application, we apply this result to branching laws for simple real Lie groups of Hermitian type. We show that the sufficient condition on multiplicity-freeness given by the theory of visible actions is also a necessary condition for holomorphic discrete series representations and symmetric pairs of holomorphic type. We also show that two branching laws of a holomorphic discrete series representation with respect to two symmetric pairs of holomorphic type coincide for sufficiently large parameters if two subgroups are in the same epsilon-family.

    DOI

    Scopus

    2
    Citation
    (Scopus)

Books and Other Publications

  • プログラミングコンテストチャレンジブック : 問題解決のアルゴリズム活用力とコーディングテクニックを鍛える

    秋葉 拓哉, 岩田 陽一, 北川 宜稔

    マイナビ  2012 ISBN: 9784839941062

  • 世界で闘うプログラミング力を鍛える150問 : トップIT企業のプログラマになるための本

    McDowell Gayle, Laakmann, Ozy, 秋葉 拓哉, 岩田 陽一, 北川 宜稔

    マイナビ  2012 ISBN: 9784839942397

Misc

  • Uniformly bounded family of D-modules and applications

    Kitagawa Masatoshi

        137 - 150  2021.11

  • Family of $\mathscr{D}$-modules and representations with a boundedness property

    Masatoshi Kitagawa

       2021.09

     View Summary

    In the representation theory of real reductive Lie groups, many objects have
    finiteness properties. For example, the lengths of Verma modules and principal
    series representations are finite, and more precisely, they are bounded. In
    this paper, we introduce a notion of uniformly bounded families of holonomic
    $\mathscr{D}$-modules to explain and find such boundedness properties.
    A uniform bounded family has good properties. For instance, the lengths of
    modules in the family are bounded and the uniform boundedness is preserved by
    direct images and inverse images. By the Beilinson--Bernstein correspondence,
    we can deduce several boundedness results about the representation theory of
    complex reductive Lie algebras from corresponding results of uniformly bounded
    families of $\mathscr{D}$-modules. In this paper, we concentrate on proving
    fundamental properties of uniformly bounded families, and preparing abstract
    results for applications to the branching problem and harmonic analysis.

  • Uniformly bounded multiplicities, polynomial identities and coisotropic actions

    Masatoshi Kitagawa

       2021.09

     View Summary

    Let $G_{\mathbb{R } }$ be a real reductive Lie group and $G'_{\mathbb{R } }$ a
    reductive subgroup of $G_{\mathbb{R } }$ such that $\mathfrak{g'}$ is algebraic
    in $\mathfrak{g}$. In this paper, we consider restrictions of irreducible
    representations of $G_{\mathbb{R } }$ to $G'_{\mathbb{R } }$ and induced
    representations of irreducible representations of $G'_{\mathbb{R } }$ to
    $G_{\mathbb{R } }$. Our main concern is when such a representation has uniformly
    bounded multiplicities, i.e. the multiplicities in the representation are
    (essentially) bounded. We give characterizations of the uniform boundedness by
    polynomial identities and coisotropic actions.
    For the restriction of (cohomologically) parabolically induced
    representations, we find a sufficient condition for the uniform boundedness by
    spherical actions and some fiber condition. This result gives an affirmative
    answer to a conjecture by T. Kobayashi.
    Our results can be applied to $(\mathfrak{g}, K)$-modules, Casselman--Wallach
    representations, unitary representations and objects in the BGG category
    $\mathcal{O}$. We also treat with an upper bound of cohomological
    multiplicities.

  • Wave front sets of matrix coefficients and the discrete decomposability

    Masatoshi Kitagawa

        19 - 32  2019.11

  • 誘導表現の重複度の一様有界性について

    北川 宜稔

    数理解析研究所講究録   2103   60 - 75  2018.02

  • Irreducible decompositions with continuous parameter and D-modules on the basic affine space

    Kitagawa Masatoshi

        64 - 73  2017.11

  • Uniformly boundedness of multiplicities and polynomial identities

    Kitagawa Masatoshi

        72 - 80  2016.11

  • 正則離散系列表現の分岐則と複素化について

    北川 宜稔

    数理解析研究所講究録   1977   77 - 90  2015.12

    CiNii

  • ユニタリー表現の分岐則と複素化について

    北川 宜稔

    表現論シンポジウム講演集     97 - 105  2014.11

  • A stability theorem for multiplicity-free varieties and its applications

    Kitagawa Masatoshi

    RIMS Kokyuroku   1877   41 - 49  2014.02

    CiNii

▼display all

Presentations

  • Uniformly Bounded Multiplicities in the Branching Problem and D-modules

    Kitagawa Masatoshi

    Presentation date: 2022.08

  • Regular holonomic g-module and branching problem

    Kitagawa Masatoshi

    Presentation date: 2022.07

    Event date:
    2022.07
     
     
  • Uniformly bounded family of D-modules and applications

    Kitagawa Masatoshi

    Presentation date: 2021.11

    Event date:
    2021.11
     
     
  • On the discrete decomposability and invariants of representations of real reductive Lie groups

    Masatoshi Kitagawa

    Presentation date: 2021.06

  • Wave front sets of matrix coefficients and the discrete decomposability

    Kitagawa Masatoshi

    Presentation date: 2019.11

  • Basic affine space 上の微分作用素のフーリエ変換と Beilinson--Bernstein 対応の一般化について

    北川 宜稔

    早稲田大学概均質セミナー 

    Presentation date: 2019.07

  • Invariant differential operators and uniformly bounded multiplicities

    Kitagawa Masatoshi  [Invited]

    Presentation date: 2019.03

  • 誘導表現の重複度の一様有界性について

    北川 宜稔

    RIMS共同研究(公開型)「表現論と代数、幾何、解析をめぐる諸問題」 

    Presentation date: 2018.06

  • Irreducible decompositions with continuous parameter and D-modules on the basic affine space

    Kitagawa Masatoshi

    Presentation date: 2017.11

  • Uniformly boundedness of multiplicities and polynomial identities

    Kitagawa Masatoshi

    Presentation date: 2016.11

  • Algebraic aspects of branching laws for holomorphic discrete series representations

    Kitagawa Masatoshi

    Presentation date: 2016.06

  • 絡作用素の空間に入る代数構造について

    北川 宜稔

    北海道大学表現論セミナー 

    Presentation date: 2016.03

  • The BGG category O and the category of generalized Harish-Chandra modules

    Kitagawa Masatoshi

    Presentation date: 2016.03

  • Classification of multiplicity-free holomorphic discrete series representations

    Kitagawa Masatoshi

    Presentation date: 2015.09

  • On the irreducibility of U(g)H-modules

    Kitagawa Masatoshi

    Analytic representation theory of Lie groups 

    Presentation date: 2015.07

  • 正則離散系列表現の分岐則と複素化について

    北川 宜稔

    RIMS研究集会「表現論および関連する調和解析と微分方程式」 

    Presentation date: 2015.06

  • On irreducibility of U(g)H-modules

    Kitagawa Masatoshi

    AGU Workshop on Geometry and Representation Theory 

    Presentation date: 2015.05

  • 部分群の複素化のみに依存する正則離散系列表現の分岐則の性質について

    北川 宜稔

    広島大学トポロジー・幾何セミナー 

    Presentation date: 2015.04

  • ユニタリー表現の分岐則と複素化について

    北川 宜稔

    2014年度表現論シンポジウム 

    Presentation date: 2014.11

  • Stable branching laws for spherical varieties

    Kitagawa Masatoshi

    East Asian Core Doctoral Forum on Mathematics 

    Presentation date: 2014.01

  • A stability theorem for multiplicity-free varieties and its applications

    Kitagawa Masatoshi

    Presentation date: 2013.06

  • A stability theorem for multiplicity-free varieties and its applications

    Kitagawa Masatoshi

    Group Actions with applications in Geometry and Analysis in honour of Toshiyuki Kobayashi 50th birthday 

    Presentation date: 2013.06

▼display all

Specific Research

  • 実簡約リー群の表現の絡作用素とルート系の関係

    2019  

     View Summary

    リー群の分岐則が、具体的な不変量によってどのように統制されるかについて研究を行った。分岐則が扱いやすい状況として、離散的に分解するという場合が存在する。本研究において、表現が離散的に分解するための条件を、 wave front set と呼ばれる表現の不変量を用いて与えた。さらに、離散的に分解したうえで重複度が有限になるという許容的になるための条件も、同様の手法により与えた。これらの結果は実簡約リー群の場合には、小林俊行氏の1994,98年における論文の一般化となっている。この研究結果は、2019年度の表現論シンポジウムにおいて発表された。

 

Syllabus

▼display all