Updated on 2022/12/04

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

• Algebra

• 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.

• 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.

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

• 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.

• 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

• 北川 宜稔

数理解析研究所講究録   ( 2031 ) 180 - 190  2017.05

• Uniformly boundedness of multiplicities and polynomial identities

Kitagawa Masatoshi

72 - 80  2016.11

• 北川 宜稔

数理解析研究所講究録   1977   77 - 90  2015.12

• 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

• Kitagawa Masatoshi

RIMS Kokyuroku   1877   41 - 49  2014.02

### 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

### Specific Research

• 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

2022   spring semester

2022   fall semester

• School of Education

2022   full year

• School of Education

2022   fall semester

• School of Education

2022   fall semester

• School of Education

2022   fall semester

• School of Education

2022   fall semester